Spherically actuated platform manipulator (Q2711925)

The authors discuss a spherically actuated parallel manipulator. It consists of a moving platform which is connected to a fixed base via two spherical-prismatic-universal chains. Only two spherical joints are actuated, both universal and prismatic joints are passive. In both direct and inverse analysis the authors have to take into account the passive joints. The inverse kinematics is solved analytically, whereas the direct kinematics is solved only numerically. The complete analytic solution of the direct kinematics remains an open problem. Especially, the number of solutions is not reported. Then the authors perform the velocity analysis, namely calculate the Jacobian operator that links Cartesian velocities of the end effector to the active joint rates. The paper ends with an example in which the authors demonstrate the inverse and forward kinematics as well as the calculation of joint rates.