A Simulation Tool for Visualizing the Assembly Modes and Singularity Locus of 3RPR Planar Parallel Robots

This paper presents a graphical and intuitive tool for simulating the forward kinematics of planar parallel 3RPR robots with arbitrary geometric design. The proposed tool allows the user to visualize the singularity locus of the robot and the evolution of all the solutions to its forward kinematic problem in the complex plane. The user can modify all the geometric design parameters of the robot and instantaneously visualize the effect of these modifications on the singularity locus. As the presented examples illustrate, the proposed tool is especially useful for visualizing the coalescence of different solutions of the forward kinematic problem when approaching higher-order singularities, as well as for visualizing how these special singularities transform when perturbing the different geometric parameters of the robot.