Using CNC Techniques to Preserve Traditional Floor Arts : A Digital Manufacturing Approach

Using CNC Techniques to Preserve Traditional Floor Arts : A Digital Manufacturing Approach

Aarav Jaisingh, Riya Swamy

Team RoboArt Squad (Team 1435), Bengaluru, Karnataka, India Mentor: Amit Jaisingh

Abstract – Traditional Indian oor arts such as rangoli and kolam are transmitted almost entirely by oral and observational means, and are consequently vulnerable to loss as demographic and lifestyle patterns change. This paper presents a low-cost Cartesian CNC platform that addresses preservation along three axes rather than one: mechanical reproduction of designs in dry pigment powder, computational acquisition of existing hand-drawn designs from paper archives, and structured transmission of drawing skill to human learners. The machine is a 2 ft × 2 ft belt-driven gantry built on 20 × 20 mm V-slot aluminium extru-sion, with steel-reinforced toothed belts actuated by three NEMA 17 stepper motors under GRBL rmware on an ATmega328P controller, with a gravity-fed powder deposition end-effector in which a tapered gate is driven by the Z axis, allowing depo-sition to be commanded through the standard motion planner without rmware modication. A toolpath generation pipeline converts vector designs into G-code using greedy circular arc regression with tangential continuity enforcement, addressing the instruction-count, planner-buffer and faceting limitations of pure linear interpolation. An ofine image processing pipeline re-constructs vector geometry from photographs of handwritten notebook pages under non-uniform illumination; a key empirical nding is that pigment-dot candidate detection must precede morphological removal of ruled lines, as the reverse ordering re-duced recoverable dot candidates from 974 to 8 on a representative page. Single-stroke sikku designs are additionally validated for traceability using Eulerian graph criteria, with routing by a generalised Hierholzer decomposition. The complete system was realised at a component cost of INR 4,000.

KeywordsCNC; cultural heritage preservation; toolpath generation; arc tting; image vectorisation; Eulerian graphs; GRBL; rangoli; kolam; educational robotics

1. Introduction

   1. Background

      Floor art occupies an unusual position among traditional In- dian craft practices. Designs known regionally as rangoli, kolam, muggu, alpana, mandana and aripana are drawn daily at domestic thresholds using dry pigment powder or rice our released between the thumb and forenger. The practice is simultaneously ubiquitous and ephemeral: a de- sign is complete for a matter of hours before being erased by foot trafc, weather or deliberate cleaning, and is redrawn the following morning.

      This impermanence is intrinsic to the art form rather than incidental to it. It also means that the corpus of designs has never existed primarily as a physical archive. Transmission occurs through daily observation, with a child watching a parent or grandparent execute a design and gradually assum- ing portions of the work. Where written records exist at all, they take the form of personal notebooks maintained by indi- vidual practitioners, typically drawn on ruled paper with dot lattices and connecting strokes recorded in pencil or ink.

   2. Problem Statement

      Two distinct preservation failures follow from this transmis- sion model.

      The rst is archival. Practitioner notebooks are private, unindexed, physically fragile, and drawn on ruled stationery whose printed rules interfere with any naive attempt at au- tomated extraction. When a practitioner dies, the notebook is frequently discarded along with other household paper. There is no systematic digital corpus of regional oor art de- signs comparable to those maintained for textile motifs or architectural ornament.

      The second failure is pedagogical, and is the more con-

      sequential. Because transmission depends on sustained daily co-presence between an experienced practitioner and a learner, it is disrupted by exactly the demographic changes now widespread in urban India: nuclear household structure, apartment dwelling without a threshold surface, dual-income time constraints, and geographic separation between gener- ations. A design corpus that is fully archived but no longer executed by anyone is preserved only in the sense that a dead language is preserved.

   3. Research Motivation

      Existing automation efforts in this domain address reproduc- tion alone. A machine that draws a design faster and more precisely than a human addresses neither failure identied above: it does not acquire the undigitised corpus, and by substituting for the learner rather than scaffolding them, it may actively accelerate the pedagogical failure it purports to remedy.

      The motivating position of this work is therefore that re- production is a necessary but insufcient component of a preservation system, and that a machine intended to preserve a living practice must additionally acquire existing artifacts and transmit executional skill.

   4. Objectives

      The objectives of this work are:

      1. To design and realise a Cartesian CNC platform capa- ble of depositing dry pigment powder on a horizontal oor surface at a component cost accessible to individual households and schools.

      2. To develop a deposition end-effector that operates within the constraints of unmodied open-source CNC rmware.

      3. To develop a toolpath generation pipeline that produces geometrically faithful and computationally compact G- code from vector designs.

      4. To develop an ofine image processing pipeline capable of reconstructing vector geometry from photographs of handwritten notebook pages.

      5. To formalise traceability constraints for single-stroke de- signs using graph-theoretic criteria.

      6. To implement and evaluate a graduated-autonomy peda- gogical mode in which machine assistance is systemati- cally withdrawn as learner competence increases.

   5. Novel Contributions

      1. A powder deposition mechanism in which the metering gate is actuated by the Z axis of a standard three-axis controller, permitting deposition timing to be scheduled by the existing motion planner without rmware modi- cation.

      2. A tangentially-chained greedy arc regression scheme for toolpath compaction, together with an analysis of the nu- merical precision required for arc endpoint consistency under GRBLs radius validation.

      3. An ofine vectorisation pipeline for ruled-paper manuscripts in which the operational ordering of dot detection and rule removal is shown to be determinative of recovery rate.

      4. A graduated-autonomy instructional model with auto- mated competence assessment and a work-allocation algorithm that distributes machine assistance non- contiguously across a design.

   6. Paper Organisation

   Sections II and III establish prior work and system archi- tecture. Sections IV and V describe the mechatronic and electronic subsystems. Sections VI through IX describe the computational framework, image processing pipeline, tool- path generation algorithms, and execution layer. Section X presents the graph-theoretic treatment of single-stroke de- signs, and Section XI the pedagogical framework. Sec- tins XII and XIII present methodology and results, followed by discussion, applications and conclusions.

2. Literature Review

   1. Digital Preservation of Cultural Heritage

      Digital heritage preservation has historically concentrated on tangible, durable artifacts manuscripts, sculpture, archi- tecture for which photogrammetric and laser-scanning ap- proaches are well established. Intangible and performative heritage has received substantially less methodological atten- tion, and ephemeral practices that leave no durable artifact are poorly served by capture-oriented frameworks. Floor art falls into this least-served category: the artifact is destroyed by design, and what requires preservation is the generative knowledge rather than any particular instance.

   2. CNC-Based Artistic Fabrication

      Cartesian plotting mechanisms for artistic output are ma- ture. Pen plotters, drawing robots and educational XY gantries are widely documented, and the underlying kine- matics, rmware and toolpath conventions are effectively

      standardised through the open-source CNC ecosystem. The specic problem of depositing loose granular material rather than marking with a pen or cutting tool is comparatively un- addressed, principally because granular ow control intro- duces failure modes arching, ratholing, stroke-end smear

      • with no analogue in subtractive or pen-based fabrication.

   3. Prior Art in Automated Rangoli Reproduction

      Three prior systems are relevant. The Rang Bot [23] imple- ments a two-axis gantry carrying a powder dispenser over a 60 cm working span, with an image-to-G-code conversion stage and dispensing regulated by a geared DC motor driv- ing a 5 mm orice. Two characteristics distinguish it from the present work. Its reported axis resolutions differ by more than two orders of magnitude between X and Y, indicat- ing a strongly anisotropic transmission; and the dispenser is driven independently of the motion controller rather than as a planner-scheduled axis, so deposition timing is not se- quenced with position by the rmware. A single dispenser is carried, and no multi-pigment workow is described.

      A separate proposal [22] addresses automated rangoli us- ing a wheeled agent with overhead optical feedback and edge-detection-based path derivation, targeting uneven sur- faces. This is a closed-loop mobile approach rather than a xed-frame CNC one, and addresses a different set of con- straints.

      It should be noted that published work in this specic application area is sparse and consists substantially of stu- dent project reports and non-archival proceedings rather than peer-reviewed literature; the comparison in Section XIII-H should be read with that in mind. Commercial stencil-based products such as the Rangoli Magic Box achieve reproduc- tion without programmability, transferring a xed pattern through a perforated template. Educational kit platforms such as those distributed by Witblox provide a programmable gantry but no domain-specic design tooling, toolpath opti- misation, or pedagogical layer.

      In each case the system boundary terminates at reproduc- tion. None of the surveyed systems acquires existing designs from physical archives, and none addresses skill transmis- sion.

   4. Computer Vision for Pattern Digitization

      Document image analysis provides well-developed tech- niques for binarisation under non-uniform illumination, no- tably adaptive and locally-adaptive thresholding, and for the removal of printed rules and form lines by directional mor- phological operation. Skeletonisation and crossing-number analysis are standard for stroke extraction from binarised handwriting.

      The specic difculty in the present domain is that the target geometry comprises two semantically distinct layers

      • a lattice of pigment dots (pulli) and the strokes drawn around them whose visual characteristics overlap substan- tially with the printed rules that must be removed. This in- teraction, addressed in Section VII, does not arise in conven- tional form-processing applications where the content to be preserved is textual.

   5. Computational Study of Kolam

      Kolam has attracted formal attention as a generative system, with published treatments as picture languages, array gram-

      mars and L-systems. This body of work establishes that ko- lam designs admit rigorous formal description, and in partic- ular that a substantial subclass the sikku or knot kolam is characterised by continuous single-stroke traversal. Ex- isting work is predominantly generative and analytical; its translation into real-time execution constraints for a physical plotting system has not been reported.

   6. Research Gap

   The literature therefore establishes mature but disjoint capa- bilities: CNC fabrication without granular deposition or cul- tural domain tooling; document vectorisation without dot- stroke layer separation; and formal kolam analysis without physical realisation. No reported system integrates acquisi- tion, reproduction and transmission within a single platform.

3. System Architecture

   1. Overall Framework

      The system comprises a three-axis Cartesian gantry with an interchangeable end-effector, an embedded motion controller executing GRBL rmware, and a host application providing design authoring, acquisition, toolpath generation and job streaming. The host application is implemented as a single- le Python program and is designed to be fully functional without network connectivity, with the exception of two ex- plicitly optional features.

   2. Preservation Model

      The architecture is organised around three functional axes, which are treated throughout this paper as coequal rather than as a primary capability with ancillary features.

      Reproduction is the execution of a vector design in physi- cal pigment on a oor surface (Sections IV, VIII, IX).

      Acquisition is the recovery of vector geometry from ex- isting physical records principally photographs of prac- titioner notebooks into an indexed digital corpus (Sec- tions VI, VII).

      Transmission is the structured conveyance of executional skill to a human learner, with machine assistance withdrawn progressively as competence increases (Section XI).

   3. Hardware Architecture

      The mechanical layer consists of a 20 × 20 mm V-slot alu- minium extrusion frame, belt-driven X and Y carriages run- ning on polymer V-wheels engaging the extrusion prole di- rectly, and a Z-actuated deposition head. The electronic layer comprises an ATmega328P-based controller, a stepper driver carrier shield, three bipolar stepper drivers and a switched- mode power supply. A USB webcam mounted above the working area provides overhead image capture for the as- sessment function of Section XI-D. Communication with the host is over USB serial.

   4. Software Architecture

      The host application maintains an internal geometric repre- sentation independent of both the input source and the output target. Seven acquisition paths built-in gallery, direct pen authoring, DXF import, generative image synthesis, photo- graphic import, photographic rangoli conversion and note- book digitisation converge on this representation, from which toolpath generation, on-screen simulation and peda- gogical decomposition all proceed.

   5. System Workow

   A complete job proceeds as: design acquisition or authoring

   geometric preprocessing arc regression and toolpath synthesis on-screen simulation serial streaming with handshake physical execution, with colour-change and re- ll interruptions scheduled as required./p>

4. Mechatronic Design

   1. Cartesian Kinematic Conguration

      A Cartesian conguration was selected over polar, SCARA or delta alternatives. The determining consideration is that the coordinate frame of the artwork is itself Cartesian in the relevant sense: oor art is authored on a square or rectangu- lar eld, dot lattices are predominantly orthogonal or rotated- orthogonal, and the mapping from design space to machine space is therefore afne with no trigonometric transforma- tion. This preserves geometric delity without accumulation of transformation error and permits the toolpath generator to emit machine coordinates by direct scaling.

   2. Structural Design

      The frame is constructed from 20 × 20 mm V-slot aluminium extrusion forming a 2 ft × 2 ft working envelope, with cor- ner junctions and carriage bodies fabricated in PLA by fused deposition modelling. This hybrid approach loads the extru- sion along its principal axis, where its stiffness-to-mass ratio is favourable, while permitting rapid iteration of the geomet- rically complex junction and carriage components at negligi- ble cost.

      The V-slot prole is structural and kinematic simultane- ously. Its chamfered channels form the linear raceway on which the carriages run, so no separate guide rail, shaft or bearing block is required. This eliminates the align- ment problem that dominates assembly of rail-and-carriage gantries at this scale, in which parallelism between an independently-mounted rail and the frame member support- ing it must be established and maintained by shimming. Here the raceway is a machined feature of the structural member itself and is parallel to it by construction.

   3. Linear Motion Transmission

      Motion on both principal axes is transmitted by toothed belt over pulleys driven directly from the stepper shafts. The car- riages are guided by polymer V-wheels running in the cham- fered channels of the extrusion, with eccentric spacers on one wheel of each carriage permitting preload against the race- way to be adjusted after assembly.

      The belts are GT2 prole, of 2 mm pitch, with steel-cord reinforcement in a polyurethane body. Reinforcement ma- terial is the principal selection consideration and warrants comment, since it determines the dominant positional error term in a belt-driven gantry.

      A toothed belt under tension elongates elastically along its free span. Because the free span between the driven pulley and the carriage varies with carriage position, this elongation produces a position-dependent error rather than a constant offset, and it reverses sign on direction change, appearing as apparent backlash. Elongation is governed by the ten- sile modulus of the reinforcing cord: steel cord is substan- tially stiffer than the glass-bre reinforcement conventional in low-cost belts, reducing this error term correspondingly.

      Steel reinforcement additionally exhibits negligible moisture absorption, so belt tension does not drift with ambient hu- midity relevant here, as the machine operates in domestic and outdoor threshold environments without climate control. The consequence for this application is specic. Floor art geometry is dominated by closed loops and by symmetric gures executed as mirrored strokes, in which the machine reverses direction repeatedly within a single design. A posi- tional discontinuity at each reversal is directly visible in the deposited line as a step in an otherwise smooth curve. Min- imising the reversal error term is therefore of greater conse- quence here than in fabrication applications where reversals

      are infrequent.

      Belt transmission was selected in preference to lead screw for three reasons. Traverse velocity is substantially higher for a given motor speed, which is material given that deposition feedrates are already constrained by powder ow behaviour (Section IX-B) and that non-depositing repositioning moves are pure overhead. Moving mass is lower, since the belt it- self contributes negligible inertia and no rotating mass scales with axis length. And axis length is not bounded by the rota- tional dynamics of the transmission element, as discussed in Section XIV-C.

      The trade-off accepted is that a belt drive is backdriv- able: an external force applied to the carriage will displace it against an unpowered motor. The gantry therefore does not hold position without holding current. In horizontal op- eration this is inconsequential, as gravity acts normal to both axes of motion. It is the governing constraint on any non- horizontal extension, and is treated in Section XV-D.

   4. Powder Deposition End-Effector

      1. Hopper geometry and arch prevention. Dry pigment powder in a converging hopper is subject to arch formation, in which interparticle friction and geometric interlocking allow a sta- ble bridge to form across the converging section, arresting ow while material remains above. Arching probability in- creases with the angle of convergence and with irregularity in the wall prole.

         The hopper adopted here uses a parabolic inner wall pro- le rather than a straight conical taper. A parabolic prole presents a continuously varying wall angle with no disconti- nuity in curvature at which a stable arch can key, and main- tains a monotonic reduction in cross-sectional area along the ow axis. Empirically, straight-cone prototypes exhibited arching requiring manual agitation, whereas the parabolic prole sustained ow without intervention across the range of commercial pigment grades tested.

      2. Tapered gate mechanism. Flow is metered at the outlet by a gate that translates vertically. The gate aperture is tapered rather than of constant section, so that gate displacement pro- duces a progressive rather than binary change in effective orice area, and so that particles trapped at the closing edge are displaced laterally rather than crushed against a square shoulder. The latter property substantially reduced jamming at stroke termination, which in constant-section prototypes produced a characteristic smear at the end of each deposited stroke.

      3. Z-axis actuation of the gate. The gate is driven by the third stepper axis, addressed as Z in the emitted G-code. This is the principal architectural decision in the end-effector design.

         Deposition could alternatively have been controlled by a servo or solenoid driven from an auxiliary output. That ap- proach was rejected because such an output is not scheduled by the motion planner: it is asserted immediately upon com- mand parsing, whereas queued motion commands execute after an arbitrary planner delay. Deposition timing would therefore lose synchronisation with position, with the error varying according to queue depth.

         By assigning the gate to a motion axis, gate transitions are enqueued in the same planner as the XY moves and ex- ecute in strict sequence with them. Gate open and close are commanded as:

         G1 Z0.0500 F150 (open) G1 Z0.0000 F150 (close)

         with the small displacement chosen to minimise transition time while remaining well above the positional resolution of the axis. No rmware modication is required, and the ar- rangement generalises directly to alternative end-effectors: a pen holder actuated on the same axis performs lift and lower, and a syringe plunger performs advance and retract, without alteration to the toolpath generator.

   5. Mechanical Calibration

      The transformation from design space to machine space is nominally isotropic. In a belt-driven axis the theoretical scale factor is determined exactly by belt pitch, pulley tooth count and driver microstepping, and requires no empirical correc- tion; residual error arises only from pulley pitch-diameter tolerance and from belt tension differences between axes.

      A per-axis scalar correction is nonetheless appied at the point of G-code emission (Section VI-A), with values de- termined by the procedure of Section XII-C. The correc- tion factors carried in the present build are Cx = 1.00 and Cy = 0.84.

   6. End-Effector Modularity

   The mounting interface and the Z-axis actuation scheme de- scribed above are medium-agnostic. Table 1 summarises the substitutions required to address related art forms outside the dry-powder oor domain; these are presented as design anal-

   ysis rather than as realised results, and are discussed further in Section XV-D.

   TABLE 1: End-effector substitution analysis

   Medium Z-axis function Toolpath change

   Dry powder (re- Gate open/close None alised)

   Ink on paper Pen lift/lower Region ll; reduced

   arc tolerance Viscous paste Plunger ad- Retraction schedul-

   vance/retract ing

5. Electronic Control System

   1. Embedded Controller Architecture

      Motion control is executed on an ATmega328P microcon- troller in an Arduino Uno form factor, running GRBL rmware. The controller performs G-code parsing, look- ahead trajectory planning, acceleration management and step pulse generation. Selection was governed by the availability of a mature, well-documented open-source rmware with a stable G-code dialect, and by unit cost and replacement avail- ability in the target deployment context.

      D. Power Management

      The system is supplied from a switched-mode power supply delivering 12 V at 10 A. Steady-state draw with three axes energised is substantially below this rating; the margin ac- commodates the transient demand during simultaneous ac- celeration on both principal axes, which is the worst case for supply loading.

      E. Communication Architecture

      The host communicates with the controller over USB serial at 115,200 baud. Protocol details, including the connection establishment sequence and ow control discipline, are given in Section IX-C.

6. Computational Framework

   1. Coordinate Transformation Model

      Three coordinate frames are maintained: a screen frame in pixels, a machine frame in dimensionless machine units, and a physical frame in millimetres.

      The machine frame spans [0, 4.7] on both axes. The cor- respondence to physical dimension is established by a single measured constant, the deposition span of the working mat, S = 240.0 mm, giving

      The principal constraint accepted with this selection is that the planner buffer and serial receive buffer are small in absolute terms, which shapes the streaming protocol de-

      S

      =

      Xmax

      240.0

      = 51.06 mm/unit (1)

      4.7

      scribed in Section IX-C.

   2. Stepper Motor Drive Electronics

      Three bipolar stepper drivers are carried on a shield inter- posed between the controller and the motors. The motors are NEMA 17 frame units of type 17HS3401, rated at 1.3 A per

      The screen-to-machine transformation accounts for can-

      vas margins and for the inversion of the vertical axis between screen convention (origin top-left, y increasing downward) and machine convention (origin bottom-left, y increasing up- ward):

      phase.

      Motor selection warrants comment. A higher-torque vari-

      m = px L X

      x W

      max

      (2)

      ant in the same frame, the 17HS4401 at 1.7 A per phase, was evaluated and rejected. The A4988 driver dissipates heat pro-

      m = H (py T ) Y

      y H

      max

      (3)

      portional to the square of the regulated coil current, and at

      1.7 A the driver entered thermal shutdown during extended jobs without forced-air cooling. The 1.3 A motor operates within the drivers passive thermal envelope while providing torque margin adequate for the gantry mass in horizontal op- eration. This margin is not adequate for vertical operation, as noted in Section XV-D.

   3. Microstepping Conguration and Current Limiting

   The drivers are congured for 1/16 microstepping by jumper selection on the carrier shield. With 1.8 motors this yields 3200 steps per revolution; driving a 20-tooth pulley on 2 mm- pitch belt gives 40 mm of carriage travel per revolution and therefore a nominal resolution of 80 steps/mm, or 12.5 m per microstep. This is an order of magnitude ner than the deposited line width and is not the limiting term in positional accuracy. Coil current is limited by adjusting the on-board reference potentiometer, which sets the peak regulated cur- rent per phase in proportion to the reference voltage and inversely to the current sense resistance of the driver car- rier. The limit was set empirically: the potentiometer was advanced until the motors held position reliably under the worst-case simultaneous two-axis acceleration, and no fur- ther, so as to remain within the passive thermal envelope dis- cussed above.

   where L and T are the left and top canvas margins and W , H the usable canvas extents in pixels.

   The forward and inverse transformations are implemented as exact functional inverses and are used throughout the ap- plication for interactive coordinate reporting. Critically, the per-axis calibration factors Cx, Cy of Section IV-E are not applied within these transformations. They are applied only at the point of G-code emission:

   gx = Cx mx, gy = Cy my (4)

   This separation is deliberate. Were calibration folded into the display transformation, a design authored on screen would be silently distorted relative to its stored representa- tion, and successive edit-and-save cycles would compound the distortion. Conning calibration to the export boundary ensures that the stored design is a faithful record indepen- dent of the calibration state of any particular machine a requirement that follows directly from the archival objective of Section I-D.

   1. Internal Geometric Representation

      A design is represented as an ordered list of shape records. Each record contains a list of paths, each path being an or- dered sequence of vertices in machine coordinates; a nomi- nal colour; and an optional per-path colour list permitting a

      single shape to carry multiple pigment assignments. Curved geometry authored as parametric curves is retained in para- metric form until toolpath generation, at which point it is re- sampled (Section VIII-B).

      This representation is deliberately minimal. It is the sole interface between the seven acquisition paths and the three consumers toolpath generation, on-screen simulation and pedagogical decomposition and its stability is what per- mits acquisition methods to be added without modication to the execution layer.

   2. Design Acquisition Framework

      Seven acquisition paths populate the internal representation:

      1. A curated built-in gallery of regional designs.

      2. Direct authoring with a pen tool supporting 2-, 4- and 8- fold mirror symmetry.

      3. DXF import, implemented over a standard CAD parsing library with a fallback raw entity scanner for malformed les.

      4. Generative image synthesis, with the resulting raster con- verted to vector geometry by contour extraction. This path requires network connectivity.

      5. Photographic import with contour tracing.

      6. Photographic conversion of an arbitrary image to a stylised rangoli rendering.

      7. Notebook digitisation, described in Section VII.

   Contour-based paths (46) share a common raster-to-

   The content comprises two semantically distinct layers. The pulli dot lattice denes the designs structural skeleton; the strokes are drawn in reference to it. Both must be re- covered, and must be recovered as distinct layers, becaus the pedagogical mode of Section XI requires the ability to deposit dots without strokes.

   Capture conditions are uncontrolled: handheld photog- raphy under domestic lighting, with perspective distortion, non-uniform illumination and variable focus.

   B. Acquisition and Normalisation

   The input image is rescaled such that its maximum dimen- sion does not exceed 1200 pixels, with upscaling of small in- puts permitted to a factor of 4.0. This bound is imposed for computational tractability on modest hardware and is well above the resolution at which dot and stroke features remain separable.

   A polarity test is then applied. Designs may be recorded as dark pigment on light paper or, in the case of chalk on slate or a dark oor surface, as light content on a dark ground. Otsus method is applied to obtain a global threshold, and the minority tone class is identied. Where the minority class is the lighter, the image is inverted, ensuring that all subsequent stages operate on a consistent dark-content-on-light-ground convention.

   C. Adaptive Thresholding

   Global thresholding fails on handheld domestic captures ow- ing to illumination gradients across the page. Adaptive Gaus- sian thresholding is applied with a neighbourhood block size scaled to the image dimensions:

   20

   vector procedure: greyscale conversion, Gaussian smooth- ing at 5 × 5, inverse binary thresholding, morphological clo- sure, connected-component contour retrieval with hierarchy,

   b = max

   (15,

   (j min(h,w) kl) I

   1l)

   (5)

   area-ranked retention of the largest components, polygonal approximation at a tolerance proportional to contour perime- ter, and uniform contraction about the centroid to provide deposition margin.

   D. Digital Archiving Methodology

   Designs are persisted in a structured local store together with provenance metadata. The archival requirement drives two design constraints noted elsewhere: the exclusion of cali- bration from the stored representation (Section VI-A), and the requirement that the acquisition pipeline of Section VII operate without network dependency, since the deployment context for notebook digitisation private homes, often in areas with intermittent connectivity cannot be assumed to have reliable network access at the moment of capture.

7. Image Processing and Vector

   Reconstruction

   A. Problem Characterisation

   The acquisition target is a photograph of a handwritten note- book page bearing a oor art design. The following proper- ties distinguish this from conventional document vectorisa- tion.

   The substrate is ruled stationery. Printed rules are of com- parable stroke width to the hand-drawn content and, being straight and regularly spaced, are readily separable by di- rectional morphology but only if they can be separated without collateral loss of content.

   where the bitwise disjunction with unity enforces the odd-

   size requirement of the neighbourhood window, and the oor of 15 prevents degeneration to a window smaller than the stroke width on low-resolution inputs. A constant offset of 10 is subtracted from the local mean. The binarised result is opened with a 3 × 3 elliptical structuring element to suppress isolated noise arising from paper texture.

   1. Ordering of Dot Detection and Rule Removal

      This subsection reports the principal empirical nding of the acquisition pipeline.

      Both ruled lines and pigment dots must be removed from the stroke layer: the rules because they are not content, the dots because they belong to a separate output layer and would otherwise be traced as spurious closed strokes. The natural implementation order clean the image rst, then detect features was found to be incorrect.

      Ruled lines are removed by morphological opening with long, thin structuring elements oriented horizontally and ver- tically, retaining only structures of substantial extent along one axis and minimal extent along the other. The difculty is that a dot lying on a printed rule is topologically connected to that rule in the binarised image. Under opening, the rule is identied as a long thin structure, and the dot being a small protrusion on it is removed as part of the same connected structure.

      Because rules on ruled stationery are regularly spaced and dot lattices are also regularly spaced, a substantial fraction of dots in any given design lie on or adjacent to a rule. On a

      representative captured page, performing rule removal before dot detection reduced the number of recoverable dot candi- dates from 974 to 8 a loss of over 99% of the structural lattice, and sufcient to prevent lattice estimation entirely.

      The pipeline therefore performs dot candidate detection on the thresholded image prior to rule removal, retains the resulting candidate set, and only then removes rules from the stroke layer. The detected dots are additionally subtracted from the stroke layer before skeletonisation, so that each fea- ture class is processed exactly once.

      The general principle that feature detection should pre- cede any morphological cleaning operation whose structur- ing element is of comparable scale to the features sought is stated here because it is likely to generalise to other ruled- substrate vectorisation problems.

   2. Dot Detection and Lattice Estimation

      Dot candidates are generated by connected-component anal- ysis with ltering on area, aspect ratio and ll ratio relative to the components bounding box, retaining approximately circular compact components. The candidate set is bounded at 500 to limit downstream combinatorial cost.

      A lattice is then tted to the candidate set. The dominant lattice orientation is estimated from the angular distribution of inter-candidate displacement vectors, and the lattice pitch from the modal magnitude of nearest-neighbour displace- ments. Candidates are assigned to lattice sites, and sites with no supporting candidate are recorded as absent rather than interpolated, since incomplete lattices occur legitimately in many designs.

   3. Perspective Correction via Grid Snapping

      Handheld capture introduces perspective distortion. Rather than estimating a homography from page corners unre- liable where the page is not fully visible or the boundary is obscured correction is derived from the tted lattice itself. The lattice provides a dense set of correspondences between observed positions and their idealised regular positions, from which the rectifying transformation is estimated and applied to the extracted stroke geometry.

      This approach exploits a property specic to the domain: the content itself contains a known-regular reference struc- ture, which conventional document images do not.

      The stroke count is bounded at 140.

      Recovered geometry is cropped to the lattice extent and smoothed by two passes of a local averaging lter, which re- moves the pixel-scale quantisation characteristic of skeleton traversal without materially displacing the stroke centreline.

      I. Output

      The pipeline returns the stroke path set, the dot positions, the estimated lattice pitch and orientation, the lattice assignment, and ags recording whether rules were detected and whether polarity inversion was applied. Dots and strokes are retained as distinct layers throughout.

8. Toolpath Generation Algorithms

   1. Geometric Preprocessing

      Toolpath generation consumes the internal representation of Section VI-B and emits G-code. Parametric curve segments are rst resampled to polylines at a xed screen-space inter- val of 1.5 pixels, corresponding to approximately 0.53 mm at the working scale. This interval is chosen to be well be- low the deposited line width, ensuring that resampling error is not resolvable in the physical output.

   2. Circular Arc egression

      Emitting a resampled polyline directly as linear interpolation moves produces a large instruction count, with three conse- quences: extended transmission time under the line-by-line handshake of Section IX-C, exhaustion of the controllers look-ahead planner buffer with consequent velocity discon- tinuity at segment boundaries, and visible faceting on large- radius curves.

      Circular arc regression addresses all three by representing a curved run as a single instruction rather than many. The tter operates greedily: from a starting vertex, it extends a candidate arc vertex by vertex, tting a circle to the accumu- lated run and testing maximum orthogonal deviation against tolerance. Extension continues while the t remains within tolerance; on failure, the arc is emitted over the longest sat- isfactory run and tting restarts from the terminal vertex.

      Governing parameters are given in Table 2. The tolerance is specied in millimetres and converted to machine units at load, so that geometric delity is dened with respect to the physical output rather than the internal coordinate system:

   1. Skeletonisation and Stroke Extraction

      Xmax

      4.7

      The stroke layer, having had rules and dots removed, is re- duced to unit-width by iterative morphological thinning. The

      Emachine = Emm ·

      = 0.35 · (6)

      S 240.0

      skeleton is then traversed by crossing-number analysis: each skeleton pixel is classied by the number of transitions in its 8-neighbourhood as an endpoint, a simple path pixel or a junction. Chains are walked from endpoints and junctions to produce an initial stroke set.

   2. Gap Bridging and Stroke Stitching

   Hand-drawn strokes captured photographically exhibit breaks arising from pen lift, ink starvation, focal blur and the subtraction of overlapping dots. Endpoints separated by less than a threshold proportional to the estimated lattice pitch are bridged, subject to an angular consistency test on the local stroke tangents at both endpoints, which prevents bridging between strokes that merely pass near one another. Bridged chains are then stitched into maximal continuous strokes.

   TABLE 2: Arc regression parameters

   Parameter Value

   Fit tolerance 0.35 mm

   Full-circle tolerance multiplier 3×

   Minimum run length 4 vertices

   Maximum radius 20.0 units

   Maximum sweep 2 0.15 rad Corner detection threshold 30

   Resampling interval 1.5 px

   The maximum radius bound rejects arcs whose curvature is so low that they are better represented as lines, avoid- ing numerically ill-conditioned centre estimates. The max- imum sweep bound prevents a near-complete circle from be- ing emitted as a single arc, where small endpoint errors pro-

   duce large angular ambiguity. The minimum run length pre- vents the tter from emitting arcs over vertex runs too short to establish curvature reliably.

   1. Tangential Continuity Optimization

      Independent per-run tting produces arcs that meet at shared endpoints but with mismatched tangents, yielding a visible angular discontinuity a kink at each junction. On smooth curves such as the lobes characteristic of sikku de- signs, these artifacts are conspicuous.

      Tangential continuity is enforced by chaining: the termi- nal tangent of each emitted arc is propagated as a constraint on the initial tangent of its successor, reducing the t at each junction from three free parameters to two. Where the poly- line exhibits a genuine corner detected by a local turn- ing angle exceeding 30 the constraint is deliberately re- leased, preserving intentional angularity.

      For closed paths, the seam tangent is initialised from the geometry preceding the seam rather than left free, prevent- ing a discontinuity at the closure point, which is otherwise the single most visible defect in a closed design.

   2. Path Sequencing Strategy

      Paths are ordered to minimise non-depositing traverse and, where multiple pigments are assigned, to minimise the num- ber of colour-change interruptions. Sequencing is performed as a grouping by pigment assignment followed by nearest- neighbour ordering within each group, which is adequate at the path counts encountered and avoids the cost of exact tour optimisation.

   3. Numerical Precision Analysis

      GRBL validates arc commands by computing the radius from the current position to the specied centre offset and compar- ing it against the radius from the centre to the specied end- point. Where these differ by more than an internal tolerance, the command is rejected with error:33.

      During development, arcs were rejected intermittently de- spite geometrically valid ts. The cause was inconsistent decimal precision in the emitted G-code: endpoint coordi- nates and centre offsets were formatted at differing numbers of decimal places, so that rounding introduced an asymme- try between the two computed radii exceeding GRBLs toler- ance.

      The resolution is to emit all coordinates and offsets at a uniform four decimal places. At the working scale of

      51.06 mm per unit, four decimals corresponds to approxi- mately 5 m, far below both the mechanical resolution of the axes and the deposited line width, so no delity is sacriced. This is recorded here because the failure presents as an in- termittent rmware error with no obvious relationship to its numerical cause.

   4. G-Code Synthesis

   The emitted job comprises an initialisation preamble estab- lishing absolute positioning and millimetre-equivalent units, a sequence of deposition passes each bracketed by gate-open and gate-close commands, colour-change and rell interrup- tions where required, and a termination sequence returning the head to origin with the gate closed. A representative ex- tract is given in Appendix E.

9. Motion Planning and CNC Execution

   1. Trajectory Planning and Interpolation

      Trajectory planning is delegated to the controller rmware, which performs look-ahead over its planner queue, comput- ing junction velocities from the angular deviation between successive segments and applying trapezoidal acceleration proles subject to congured maxima. Linear moves are interpolated by Bresenham-equivalent step distribution; arc moves are decomposed internally into linear segments at a rmware-congured chord tolerance.

   2. Feedrate Scheduling

      Deposition quality is dependent on the ratio of traverse veloc- ity to powder mass ow rate: excessive velocity yields a thin or broken line, insufcient velocity yields over-deposition and loss of edge denition. Because mass ow varies with pigment grade, humidity and hopper ll level, feedrate is ex- posed as a user selection rather than xed. Five settings are provided, from F 50 to F 250, with F 150 as default. The gate axis operates at a xed F 150 independent of the traverse se- lection.

   3. Real-Time Command Streaming Protocol

      Connection establishment requires a delay of approximately two seconds following port opening, during which the con- troller completes its reset sequence and emits a startup ban- ner; commands transmitted during this interval are lost. The host therefore waits, transmits a paired carriage-return- linefeed sequence to elicit the banner, and ushes the input buffer before beginning transmission.

      Streaming proceeds by strict line-by-line handshake: one command is transmitted and no further command is sent until an acknowledgement is received. Character-counting proto- cols achieve higher throughput by maintaining the receive buffer near capacity, but complicate the abort path, since buffered commands continue to execute after an abort is is- sued. Given that an aborted job here means pigment already deposited on a oor, deterministic abort bhaviour was pri- oritised over throughput. A silence timeout of 90 s terminates the job where no acknowledgement is received, this bound being set above the longest single-command execution time.

   4. Deposition Control and Colour Sequencing

      The hopper holds a single pigment at a time. Multi-colour designs are executed by grouping paths by pigment, ordering groups to minimise changes, and suspending the job at each boundary for manual hopper reloading.

      A dedicated rell position is dened at machine coordi- nate (5.00, 0.00) outside the 4.7-unit working envelope so that the head is clear of the artwork during reloading and any spillage or residual discharge falls outside the deposition area. A dwell of 5 s follows resumption before deposition recommences, allowing ow to stabilise.

   5. Fault Handling and Recovery

   Three interruption paths are provided. Pause transmits the real-time feed hold character (!), which decelerates the ma- chine to rest with the planner state intact. Resume trans- mits the cycle start character (~). Cancellation transmits a feed hold followed by soft reset (0x18), clearing the plan- ner queue and returning the controller to an idle state; the gate is commanded closed before reset to prevent continued

   discharge.

10. Mathematical Modelling

    edges. At the design complexities encountered typically fewer than several hundred edges total analysis time is negligible relative to toolpath generation.

    1. Graph-Theoretic Representation

       A signicant subclass of kolam the sikku or knot kolam

       • is dened by the property of being drawn as a single con- tinuous stroke that returns to its origin, weaving around the pulli lattice without lifting the hand. A design that cannot be so drawn is not a well-formed sikku kolam.

         This property is directly testable. The design is converted to a multigraph in which stroke intersections and endpoints become vertices and stroke segments become edges. Ver- tex identication requires tolerance, since hand-authored and photographically-acquired geometry does not produce ex- actly coincident endpoints; endpoints within 2% of the de- signs bounding span are welded to a common vertex. Dot as- sociation uses a separate threshold of 0.9 of the lattice pitch.

    2. Eulerian Traversability Analysis

       The single-stroke property is precisely the existence of an Eulerian circuit. By Eulers theorem, a connected multigraph admits an Eulerian circuit if and only if every vertex has even degree, and an Eulerian path if and only if exactly two ver- tices have odd degree.

       Let O denote the number of odd-degree vertices in a con- nected component. Then:

       1 O = 0 (closed circuit)

11. Pedagogical Framework for Skill

    Transmission

    1. Rationale

       The position advanced in Section I-C that reproduction alone does not constitute preservation of a living practice

       • is operationalised here. A machine that executes designs on demand substitutes for the practitioner. The instructional mode inverts this: the machines role is to be progressively eliminated.

    2. Graduated Autonomy Model

       Five levels are dened, differing in the proportion of a design executed by the machine. Table 3 gives the allocation.

       TABLE 3: Machine assistance by instructional level

       Level Designation Machine share

       1. Guided 0.70

       2. Assisted 0.55

       3. Shared 0.40

       4. Supported 0.20

       5. Pulli Mode 0.00

          to the condition of an independent practitioner, for whom the

          At Level 5 the machine deposits only the pulli lattice the structural scaffold and the learner executes all strokes.

          (Gi) =

          1 O = 2

          trails

          (open path)

          (7)

          This is the terminal state of the progression, and corresponds

          rO/21 O > 2

          L

          and for a design comprising components G1 … Gk, the min- imum number of pen-down strokes is i trails(Gi).

    3. Minimal Trail Decomposition and Routing

       Routing employs a generalised Hierholzer construction. Traversal begins at an odd-degree vertex where one exists, and at an arbitrary vertex otherwise. The algorithm walks unused edges until no unused edge remains at the current vertex, then splices closed sub-loops discovered from ver- tices along the completed walk. Where the walk terminates at a vertex other than its origin, the sub-walk is emitted as a separate trail rather than discarded.

       This yields both the minimum stroke count and an explicit ordering, which is used directly for toolpath sequencing and additionally rendered on screen as an animated traversal for instructional purposes.

    4. Topological Validation

       The analysis provides validation feedback at authoring time. A design intended as a sikku kolam but yielding more than one trail is reported to the author together with the loca- tions of the odd-degree vertices responsible, which corre- spond precisely to the points at which the intended single stroke is broken. This converts a stylistic property that would otherwise be veried by eye into a checkable constraint.

    5. Complexity Analysis

    Multigraph construction is O(n2) in the number of candidate vertices under naive pairwise welding, reducible by spatial indexing. Hierholzers algorithm is O(|E|) in the number of

    dot lattice is a conventional preparatory step rather than as- sistance.

    1. Work Allocation Algorithm

       Given a design decomposed into n parts and a target machine share s, allocation follows three rules.

       The machine always executes part 0. The learners rst observation in any session is therefore a complete, correctly- executed exemplar.

       The minority side is distributed rather than assigned con- tiguously. Where the machine share is below one half, machine-executed parts are spread across the design rather than concentrated; where it is above one half, learner parts are spread. Contiguous allocation would produce a design half-executed in one region and half in another, from which the learner receives no local reference for the portion they are executing. Distributed allocation ensures that adjacent com- pleted geometry is available as a reference at every point.

       The learner always retains at least one part, at every level including Level 1.

    2. Automated Skill Assessment

       Image capture for assessment is performed by a USB web- cam mounted on the frame above the working area and ad- dressed directly by the host application, rather than by hand- held photography.

       This is a deliberate departure from the acquisition pipeline of Section VII, which is explicitly designed to tolerate hand- held capture under uncontrolled conditions. The require- ments differ. Acquisition operates on artifacts that already exist in arbitrary settings, so robustness to poor capture is unavoidable. Assessment operates on a design executed on

       the machines own bed moments earlier, so the capture ge- ometry is known in advance and can be xed.

       Fixing it yields three properties that handheld capture can- not provide. The camera pose relative to the deposition bed is constant, so the homography between image coordinates and machine coordinates is established once at installation and reused, removing the per-capture perspective estimation of Section VII-F and its associated failure modes. The cor- respondence between the captured image and the reference geometry is therefore metric, permitting deviation to beeval- uated in millimetres at specic lattice positions rather than assessed only as an overall visual impression. And capture is unattended: a learner mid-session need not locate a phone, frame the shot and upload it, which is a material considera- tion where the intended learners are children.

       The mounting position is constrained by the deposition head, which must not occlude the eld of view. The head is therefore commanded to the rell position at (5.00, 0.00) already outside the working envelope for the reason given in Section IX-D before capture is triggered.

       The camera is mounted approximately 800 mm above the deposition surface and connected to the host by a USB Type- A extension lead, the frame-mounted position being beyond the reach of the cameras captive cable. At that standoff the 240 mm deposition span subtends a comfortable fraction of the eld of view of a typical webcam lens, so the design is captured without the barrel distortion that a shorter standoff and wider effective angle would introduce.

       Assessment is performed by a vision-language model against the reference geometry, returning a score on a ten- point scale with structured feedback on line continuity, sym- metry and lattice adherence. This path requires network con- nectivity.

       Where the model is unavailable, a deterministic fallback verdict is issued so that the session may complete. Fallback verdicts are recorded with an explicit provenance marker and are excluded from level progression calculations. This ex- clusion is important: a fallback verdict carries no evidence about learner competence, and permitting it to inuence pro- gression would allow level changes driven by network con- ditions rather than performance.

    3. Progression Criteria

       Progression is evaluated over a sliding window of the two most recent assessed attempts. Promotion requires both at- tempts in the window to score at least 8.0; demotion follows where both fall below 5.0. Requiring consistency across two attempts rather than acting on a single result prevents oscil- lation driven by individual anomalous sessions.

    4. Symmetry-Based Instruction

    Symmetry is treated as an explicit instructional dimension, with the order of symmetry increasing across levels from 2- fold through 4-fold to 8-fold. At each order, the learner ex- ecutes only the fundamental domain the half, quadrant or octant from which the complete design is generated by re- ection with the machine generating the remainder. This

    makes the generative structure of the design explicit rather than leaving it to be inferred, and reuses the same transfor- mation engine that implements the mirror pen tool of Sec- tion VI-C.

12. Experimental Methodology

    1. Experimental Setup

       Testing was conducted on a level tiled oor, chosen for its atness and for the visual contrast it provides against light- coloured pigment. Positional measurements were taken with a vernier caliper of 0.02 mm resolution, which is an order of magnitude ner than the expected deviations and therefore does not limit the reported gures.

       Four deposition media were used across testing: com- mercially available coloured rangoli powder, rice our, dry kolam maavu, and coloured sand. These span a consider- able range of particle size, density and cohesion from the ne, low-cohesion market powders through rice our, which is ner still and more prone to bridging, to coloured sand, which is coarse and free-owing. All four were dispensed by the parabolic hopper and tapered gate without mechanical agitation or modication of the end-effector.

       This is reported as a robustness observation rather than a controlled study: the media were not characterised for par- ticle size distribution, and ow rate was not measured per medium. It nonetheless indicates that the hopper geometry of Section IV-D is not tuned to a single material, which is rel- evant given that regional practice varies in the medium used.

    2. Performance Metrics

       The following metrics are dened for evaluation:

       • Positional accuracy: deviation between commanded and achieved position, measured at lattice reference points across the working envelope.

       • Repeatability: dispersion of achieved position over re- peated approaches to the same commanded point, eval- uated separately for unidirectional and bidirectional ap- proach.

       • Geometric delity: maximum orthogonal deviation of the deposited line from the commanded path.

       • Toolpath reduction: ratio of emitted instruction count with arc regression enabled to that with linear interpo- lation only, over a xed design corpus.

       • Execution time: wall-clock job duration under both con- ditions above.

       • Digitisation recovery rate: proportion of ground-truth dots and strokes correctly recovered from captured note- book pages.

    3. Calibration Procedure

    Per-axis calibration factors are determined by commanding a traverse of known extent in machine units, measuring the achieved physical displacement, and computing the ratio. The procedure is repeated across the working envelope to conrm that the error is proportional rather than offset in

    character. Measurements were taken with the vernier caliper described in Section XII-A

13. Results and Performance Evaluation

    1. Positional Accuracy

       Deviation between commanded and achieved position was observed to fall in the range 13 mm across the working en- velope. This is an indicative gure from routine operation rather than the outcome of a controlled measurement cam- paign, and is reported as such.

       Relative to the 240 mm deposition span this represents ap- proximately 0.41.3% of full scale. It substantially exceeds the 12.5 m microstep resolution of Section V-C, conrming that stepping resolution is not the limiting term; the dominant contributions are expected to be belt elongation and reversal error (Section XIV-B). It is, however, of the same order as the deposited line width, so the error is at the threshold of visibility in the physical output rather than well below it.

    2. Repeatability

    3. Geometric Fidelity

    4. Toolpath Compaction

       Arc regression is retained on the grounds given in Sec- tion VIII-B: a curved run is emitted as one instruction rather than many, which reduces transmission time under the line- by-line handshake, reduces pressure on the controllers look- ahead buffer, and removes visible faceting on large-radius curves. A controlled comparison of instruction count and job duration with regression enabled and disabled was not per- formed, and no quantitative reduction is claimed here. Such a comparison is identied as immediate further work in Sec- tion XV-E.

    5. Digitization Accuracy

       The pipeline was evaluated on a set of captured notebook pages spanning differing lighting conditions, substrates and design complexities. For each page, ground truth was es- tablished by manual inspection of the original photograph, counting the pulli dots and the distinct strokes visible to a human reader. Pipeline output was then compared against this ground truth.

       A recovered dot was counted as correct where it fell within half a lattice pitch of a ground-truth dot; a recovered stroke was counted as correct where it followed the same route between the same lattice positions as a ground-truth stroke, allowing for the smoothing of Section VII-H. Recov- ered features with no ground-truth counterpart were counted as false positives.

       TABLE 4: Digitisation recovery by page

       Dots Strokes

       <3>Pg Condition GT Rec. GT Rec. FP Rec.%

       1

       2

       3

       4

       5

       6

       7

       8

       9

       10

       Mean

       GT: ground truth by manual inspection. Rec.: correctly recovered. FP: false positives. Condition: describe substrate and lighting, e.g. ruled, daylight or unruled, indoor lamp.

       The ordering effect of Section VII-D was quantied sepa- rately on a representative page: dot candidates recovered fell from 974 under detection-before-rule-removal to 8 under the reverse ordering, a reduction of over 99%.

    6. Computational Performance

       The digitisation pipeline completes in approximately 15 s per page on the host described below, which is well within the tolerance for an interactive acquisition workow and does not constitute a practical constraint on archiving throughput.

       The host is a macOS laptop

    7. Comparative Analysis

    Table 5 positions the system against the prior art surveyed in Section II-C.

    TABLE 5: Comparison with prior systems

    Capability	Stencil	RangBot	Kit	This
    Powder deposition
    User design authoring
    Toolpath optimisation
    Multi-pigment
    Archive acquisition
    Skill transmission

14. Discussion

    1. Engineering Trade-offs

       Three selections traded performance for properties judged more material to the application.

       Belt transmission was adopted in exchange for traverse velocity, low moving mass and unbounded axis length, at the cost of backdrivability and of a position-dependent elonga- tion term absent in screw drives. The latter is mitigated but not eliminated by steel-cord reinforcement.

       Line-by-line streaming was adopted at a cost in through- put, in exchange for deterministic abort behaviour justi- ed by the irreversibility of deposition onto a oor.

       The lower-current motor variant was adopted at a cost in torque margin, in exchange for operation within the drivers passive thermal envelope, avoiding forced-air cooling and its associated cost, noise and disturbance of deposited powder.

    2. Sources of Error

       Positional error arises from four sources. Belt elongation un- der tension varies with the free span between pulley and car- riage and therefore with carriage position, reversing sign on direction change; steel-cord reinforcement reduces this term but does not remove it. Pulley pitch-diameter tolerance pro- duces a proportional scale error, addressed by per-axis cali- bration. Tooth engagement backlash contributes a small re- versal error, minimised by belt preload. Step loss under tran- sient load is undetectable in an open-loop conguration.

       Deposition error arises from variation in mass ow with hopper ll level, since the discharge rate of a gravity-fed hopper is weakly dependent on head height, with ambient humidity, which alters interparticle cohesion, and with the medium itself, since the four materials of Section XII-A dif- fer in bulk density and therefore in mass discharged per unit time at a given gate opening.

       Acquisition error arises principally from lattice estimation failure on designs with sparse or highly irregular dot place- ment, where insufcient candidates survive ltering to estab- lish pitch and orientation reliably.

    3. Scalability

       The working envelope is xed by the frame. Belt transmis- sion scales more favourably in length than a screw drive, since no rotating element spans the axis and the critical-speed limit that bounds long screws does not arise; enlargement re- quires only longer extrusion and belt. The limiting factors at increased length are instead belt sag under its own weight in long unsupported spans, which requires intermediate sup- port or increased tension, and the reduction in rst natural frequency of the extended span, which lowers the accelera- tion achievable before excitation of frame resonance.

    4. Limitations

    The system is open-loop; no position feedback is available, and step loss is therefore undetected. Only a single pigment may be loaded at any time, so multi-colour designs require manual intervention. The digitisation pipeline requires rea- sonably diffuse illumination and fails on strongly specular or heavily creased substrates. The instructional framework has been used by more than ten learners over a period of several week

    These sessions were conducted as informal use rather than as a controlled study: there was no control group, no pre- and post-test instrument, and no blinding. The results reported therefore concern system behaviour and learner en- gagement, and do not support claims regarding learning out- comes.

15. Applications and Future Work

    1. Digital Cultural Heritage Preservation

       The acquisition pipeline enables systematic digitisation of practitioner notebooks into an indexed, searchable corpus

       with regional provenance material that is currently held privately and lost on disposal.

    2. Educational Deployment

       The instructional mode addresses the transmission failure di- rectly in contexts where daily co-presence with an experi- enced practitioner is unavailable, and is suitable for school and community-centre deployment given the component cost reported in Section XVI.

    3. Institutional Automation

       Temples, cultural institutions and hospitality venues execute oor designs at daily or event frequency, currently by skilled manual labour under time pressure. The system addresses this reproduction requirement without displacing the trans- mission function, which is served separately.

    4. Extension to Additional Art Forms

       The end-effector modularity of Section IV-F suggests ex- tension beyond dry-powder oor art. Pigment-on-substrate forms such as Madhubani require a spring-loaded pen car- rier, hole-aware contour extraction with even-odd ll deter- mination, and hatching or inward-offset ll generation, none of which exist in the present toolpath generator; the arc tol- erance would also require reduction from 0.35 mm, which is imperceptible under a powder line but not under a ne pen.

       Wall-executed forms such as Warli require vertical mount- ing, which the present transmission does not support with- out modication. Because a belt drive is backdrivable (Sec- tion IV-C), the gantry would descend under its own weight whenever the vertical-axis motor is unpowered includ- ing during the idle intervals between jobs and following any fault-induced reset. Three remedies are available: a counter- weight or gas spring offsetting the head mass, so that the net static load on the belt approaches zero; a fail-safe electro- magnetic brake on the motor shaft; or a change of transmis- sion on the vertical axis alone to a non-backdrivable screw. The rst is the least costly and the most consistent with the platforms cost objective.

       Continuous holding current is not an adequate remedy, as it provides no protection during power interruption and im- poses a sustained thermal load on a driver already operating without forced-air cooling (Section V-B).

       Vertical operation additionally requires a stepper-driven syringe extruder for viscous aste and standoff compliance to accommodate surface irregularity. The torque margin of the selected motor is a further limiting consideration, as the vertical axis must accelerate the head mass against gravity rather than normal to it.

       These extensions are presented as analysis. No non- powder output has been produced, and the claims of this pa- per are conned to the dry-powder oor domain.

    5. Further Work

    A controlled comparison of toolpath compaction instruc- tion count and job duration with arc regression enabled and disabled, over a xed design corpus would quantify a ben- et currently argued only on structural grounds. Closed-loop position feedback would permit step-loss detection. Wire- less streaming would remove the tethered host requirement. A multi-hopper carousel would eliminate manual pigment changes. Controlled evaluation of the instructional frame-

    work at adequate scale and duration is required before any claim regarding learning outcomes can be advanced.

16. Conclusion

This paper has presented a low-cost Cartesian CNC plat- form for the preservation of traditional Indian oor arts, con- structed around the position that preservation of a living prac- tice requires acquisition and transmission in addition to re- production.

The mechatronic contribution is a powder deposition end- effector whose metering gate is actuated by the Z axis of an unmodied three-axis controller, obtaining planner- scheduled deposition timing without rmware modication, and generalising to alternative media by substitution of the end-effector alone.

The algorithmic contributions are a tangentially-chained greedy arc regression scheme for toolpath compaction, to- gether with the numerical precision discipline required for arc endpoint consistency; and an ofine vectorisation pipeline for ruled-substrate manuscripts in which the order- ing of dot detection relative to morphological rule removal is shown to be determinative, with recovery falling from 974 to 8 candidates under the incorrect ordering.

Single-stroke designs are additionally validated against Eulerian criteria with routing by generalised Hierholzer de- composition, converting a stylistic property into a checkable constraint.

The system was realised at a component cost of INR 4,000, within reach of individual households and schools in the target deployment context.

The instructional framework, in which machine assistance is systematically withdrawn to a terminal state at which the machine deposits only the structural lattice, is reported as an implemented mechanism. Its efcacy is not established by this work and requires controlled evaluation at scale.

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22. J. SenGupta and S. Deb, Smart structure for automated ran- goli, in Proc. International Conference on Emerging Re- search in Computing, Information, Communication and Ap- plications (ERCICA), 2015.

23. M. Agarwal et al., The Rang Bot: A precision rangoli making robot, student project report, 2020. [Online]. Avail- able: https://mrinalsproject.wordpress.com/2020/07/31/the- rang-bot

Appendix A: Machine Parameters

Working envelope 4.7 × 4.7 units

Mat deposition span 240.0 mm

Scale factor 51.06 mm/unit

Frame 2 ft × 2 ft, 20 × 20 V-slot

Transmission Steel-cord toothed belt Guidance Polymer V-wheels on prole Calibration Cx, Cy 1.00, 0.84

Gate open / closed (Z) 0.0500 / 0.0000

Gate feedrate F 150

Rell position (5.00, 0.00)

Rell dwell 5 s

Motors NEMA 17, 17HS3401, 1.3 A/phase

Drivers A4988

Supply 12 V, 10 A SMPS

Belt GT2, 2 mm pitch, steel cord

Pulley tooth count 20T, both axes Microstepping 1/16

Nominal resolution 80 steps/mm (12.5 m)

Assessment camera USB webcam, frame-mounted Camera mounting height 800 mm above bed Camera model / resolution

Motion platform subtotal INR 3,250

Assessment camera INR 750

Total component cost INR 4,000

Appendix B: GRBL Configuration

Appendix C: Algorithm Parameters

Appendix D: Serial Protocol

$100, $101 (X, Y steps/mm) 80 (nominal, from Sec. V-C)

$102 (Z steps/mm)

G21 G90

Appendix E: Sample Toolpath

$110, $111 (max rate)

$120, $121 (acceleration)

$130, $131 (max travel)

G0 X0.0000 Y0.0000 G1 Z0.0500 F150

G1 X1.2400 Y0.8830 F150

G2 X2.1150 Y1.4420 I0.4380 J0.2790 G2 X2.9880 Y0.8830 I0.4370 J-0.5590 G1 X4.2280 Y0.0000

G1 Z0.0000 F150

G0 X5.0000 Y0.0000 G4 P5

…

G1 Z0.0000 F150

G0 X0.0000 Y0.0000