Design, Kinematic Control, and Implementation of a LEGO-Based Drawing Robot for Lissajous Curve Generation

Lissajous figures are frequently studied and widely used objects in engineering and physics. Although these patterns are usually analysed using computer simulations or oscilloscopes, such tools may limit their educational value by covering the core physical processes that generate the curves. In order to address these problems, the design, kinematic validation, and prototyping of a dual-axis drawing robot were carried out on the LEGO Education SPIKE Prime platform. The hardware implementation centres on a LEGO-based dual Scotch yoke mechanism, which supports precise transformation of uniform circular motion into simple harmonic motion. This setup implements the superposition of two independent simple harmonic oscillations by simultaneously moving the paper tray along the x-axis and the pen along the y-axis. High-fidelity trajectories are achieved through a 40:1 worm gear reduction, which enables precise control of the parameter configuration. The phase shift can be manually set by adjustment levers. The robot’s geometry supports discrete amplitude settings of 8, 16, and 24 mm by adjusting the crankpin position. System control is managed by Python code that synchronises motor speeds and angular displacements according to frequency ratios. The research methodology used the Double Diamond design thinking framework, structuring development into four phases: identifying historical mechanical solutions, defining pedagogical and technical classroom requirements, iteratively developing the LEGO prototype, and testing the system through representative drawing experiments. Results show that the robot can reproduce a broad range of periodic Lissajous curves with high repeatability, and that its physical outputs show strong visual and mathematical correspondence to ideal trajectories simulated in the Desmos graphing calculator. The final prototype satisfies classroom constraints, providing a transparent, low-cost, modular STEAM tool that bridges the distance between abstract parametric equations and complex mechanical implementations.