Spirograph Toy Modelling Using Two-Link Planar Robotic Arm in Matlab

This paper presents modelling of a physicalSpirograph Toy, a mathematical instrument for the curve generation of roulette family, using two-link planar robotic arm whose forward kinematic equations can yield parametric equations of the trochoid or spirographic family of curves if both joints are rotated simultaneously respecting a proportional relation.The software version of spirograph toy was simulated in MATLAB using two-link planar robotic manipulator having all joints revolute type and spirograph curves were obtained for different parameters values.Here cases of different patterns of spirograph curves such as hypocycloid, hypotrochoid, epicycloid and epitrochoid are dealt with examples.The generated curves were found in agreement with that of generated by parametric equations and a physical spirograph toy.The implemented soft version of spirograph provides scope for selecting multiple trace points at different positions, even beyond the region of rolling disc, simultaneously which is not possible with the physical spirograph toy.In the digital version of spirograph, it has been found possible to draw a fixed-frame crossing spirograph which is not possible to complete with the physical spirograph toy and this practicability makes digital version of spirograph superlative while providing feeling of physical spirograph motion in the course of obtaining spirograph drawings.The proposed robotic model was also used to draw spirograph of fixed size but of the same shape as that of produced by spirographic motion using inverse kinematics and Affine transform.Such a model can be used further to make spirographs on wood frame or walls for decoration.