Kinematic Analysis of a Serial Manipulator Leg for a Spherical Parallel Robot with Three Coaxial Revolute Joints

This paper presents a detailed kinematic analysis of a single leg of a 3-DOF spherical parallel robot with coaxial input links. The analysis focuses on determining the fundamental quantities, including the position, velocity, and acceleration of the end-effector. Forward kinematics is employed to derive the position and orientation of the spherical platform based on the known input joint angles. To address this problem, the homogeneous transformation matrix method is applied to establish and define the local coordinate frames, thereby constructing a clear geometric relationship between the links and the spherical platform. This approach not only simplifies the computational process but also provides a rigorous foundation for a deeper investigation of the kinematic characteristics of the mechanism. In addition, the determination of the workspace represents another important aspect of the study. The positional workspace of the end-effector is described as the set of all achievable positions during operation, while its orientation is defined as the direction from the center of rotation to these positions. Through this analysis, the obtained workspace enables the evaluation of motion limits, orientation capability, and the effective range of the mechanism. Such results are essential for validating the practical applicability of the robot in tasks requiring high precision, while also providing valuable data for subsequent studies on dynamics and control system design.