Position Kinematics of a 3-PaSR Parallel Robot for Micro Positioning Tasks

This study explores the direct kinematics problem of a 3-PaSR parallel robot. The system consists of a moving platform connected to the base by six legs, each attached at distinct points. These legs converge at only three points on the manipulator. The equations needed to solve the problem are derived from the geometric constraints imposed by the robot’s kinematic architecture, which restrict the platform’s mobility relative to the base. The resulting system of trigonometric equations is reduced to an eighth-degree polynomial, leading to up to 16 possible valid poses. The reduction of unknowns is achieved by computing the resultants of polynomial equations, determined from the corresponding Sylvester matrices.