Case of Study: Kinematics Analysis, Workspace, Simulation and Trajectory Planning of a 4-Axis Serial Robot

Abstract

Selective Compliance Assembly Robot Arm (SCARA) manipulators are extensively employed in automated manufacturing due to their ability to deliver high-speed, precise, and repeatable motion in assembly tasks. This study presents kinematic modeling and validation of a four-degree-of-freedom SCARA with an RRPR (Revolute-Revolute-Prismatic-Revolute) configuration. The forward and inverse kinematic equations were formulated by applying the Denavit-Hartenberg convention, with algebraic and geometric approaches to ensure accurate mapping between joint parameters and end-effector positions. The accuracy of the kinematical models was validated in a MATLAB-based simulation environment with the GUIDE interface, enabling visualization of joint behavior and end-effector trajectory in a 3D workspace. A full factorial design experiment (3³), consisting of 27 joint parameter combinations, assessed the positional output (Px, Py, Pz) under different configurations. In addition, optimal trajectory planning moved the robot between specified points in 4.5 seconds using a fixed time step and 451 interpolated points. Cross-validation using RoboAnalyzer demonstrated high fidelity in spatial and temporal trajectory generation. Finally, a workspace simulation with 250,000 random joint variable samples confirmed the complete workspace and mechanical constraints of the manipulator. The MATLAB workspace boundary closely agreed with RoboAnalyzer, validating the derived kinematic model for robotic motion analysis and industrial automation applications.