Kinematics and force analysis of a 6 degrees of freedom 3-UPS mechanism with triangular platform for haptic applications

This paper presents inverse dynamics equations for a 3-UPS mechanism using virtual work principle. This mechanism has three UPS legs connecting the base to a triangular platform. By changing the orientation of leg´s actuators a non-symmetric mechanism with a suitable workspace near the origin without any singularity is obtained. Direct and inverse kinematics Jacobian matrices of the mechanism are obtained by the Newton-Euler approach. Then the inverse dynamics problem is solved using the principle of virtual work, so that the force and torque of active actuators have been obtained by having external forces (force and torque) acted on the platform. Force analysis of the 3-UPS mechanism has been done in the whole workspace without any singularity. Studying several situations of the platform shows that the ranges of the magnitudes of the forces and torques of the active actuators in this mechanism are reasonable, and typical actuators can support them.