A foldable seven degrees-of-freedom four-legged parallel manipulator

This paper reports a four-legged parallel manipulator with a foldable platform. The foldable platform is connected to the fixed platform through four rRPS-type limbs. Four linear and three rotary actuators assembled near to the fixed platform provide a combined scheme of actuation allowing to ameliorate the presence of singular postures of the robot. The robot may be used as a kinematically redundant parallel manipulator where one of the two links of the foldable platform plays the role of moving platform or as a robot capable to grasp objects using a reconfigurable triangle. The inverse-forward displacement analysis is performed solving the corresponding closure equations applying numerical methods such as the Newton-homotopy method. Thereafter, the instantaneous kinematics of the foldable parallel manipulator is addressed by resorting to reciprocal screw theory. To this end, the velocity joint rate of the foldable platform is integrated to the velocity state of the moving platform yielding a seven-component vector. Naturally, a similar procedures is followed for the acceleration state of the moving platform. Finally, to show the suitability of the formulae developed for the kinematic analysis of the foldable parallel manipulator, numerical applications are included with special emphasis on the analysis of the reconfigurable triangle.