This paper presents the direct and inverse kinematics solutions for a 3-DOF special 3-PSP parallel manipulator. The 3-PSP mechanism consists of two rigid bodies, a movable platform (formed like a star) and a fixed base that are connected to each other by means of three PSP legs. For the direct kinematics, unlike traditional methods which use constraint equations and numerical methods, a novel approach is used to formulate the direct kinematics problem. The approach uses relatively simpler geometric relations and results in a closed form solution with unique answer. This enables implementation of control methods requiring fast computation times. Manipulator’s structural properties also lead us to formulate nine coupled trigonometric constraint equations that are utilized in inverse kinematics analysis. Additionally, two relevant inverse kinematics formulations are investigated. The first formulation uses xyz coordinate of tool that leads to an exact solution with multiple answers. The second formulation uses orientation of the platform as well as its z coordinate which also leads to an exact solution with unique answer.

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