Kinematic analysis of the 3-CUP parallel mechanism

•We present closed form solutions to the position and velocity analysis of the 3-CUP parallel mechanism.•Numerical examples and simulations validate the analytical results.•The parasitic motion workspace is presented.•The singular configurations of the mechanism are analyzed using screw theory.

This paper investigates the kinematics of a parallel mechanism that is composed of three identical CUP legs evenly distributed on the fixed base. The platform of the mechanism has three degrees-of-freedom, namely: two rotations and one translation along the axis perpendicular to the base. The paper obtains closed form solutions for the inverse and forward kinematics problems. Furthermore, the Jacobian matrix is determined in order to solve the instantaneous kinematics analysis. It is used for the identification of the singular configurations of the mechanism, which are investigated by applying screw theory. The parasitic motions of the platform are determined by means of a workspace analysis. This paper uses several simulations and numerical examples to prove the accuracy of the analytical results.