This paper proposes an iterative algorithm to solve the inverse displacement for a hyper-redundant elephant’s trunk robot (HRETR). In this algorithm, each parallel module is regarded as a geometric line segment and point model. According to the forward approximation and inverse pose adjustment principles, the iteration process can be divided into forward and backward iteration. This iterative algorithm transforms the inverse displacement problem of the HRETR into the parallel module’s inverse displacement problem. Considering the mechanical joint constraints, multiple iterations are carried out to ensure that the robot satisfies the required position error. Simulation results show that the algorithm is effective in solving the inverse displacement problem of HRETR.

In this work, the 3-RPRR, a new kinematically redundant planar parallel manipulator with six-degrees-of-freedom, is presented. First, the manipulator is introduced and its inverse displacement problem discussed. Then, all types of singularities of the 3-RPRR manipulator are analysed and demonstrated. Thereafter, the dexterous workspace is geometrically obtained and compared with the non-redundant 3-PRR planar parallel manipulator. Finally, based on a geometrical measure of proximity to singular configurations and the condition number of the manipulators' Jacobian matrices, actuation schemes for the manipulators are obtained. Different actuation schemes for a given path are obtained and the quality of their actuation schemes are compared. It is shown that the proposed manipulator is capable of following a path while avoiding the singularities.