Torque distribution optimization of redundantly actuated planar parallel mechanisms based on a null-space solution

Abstract

Redundant actuation for the parallel kinematic machine (PKM) is a well-known technique for overcoming general drawbacks of the PKM by helping it to avoid singularity and enhance stiffness characteristics, among others. Torque distribution plays a critical role in redundant actuation because this actuation causes the PKM to consume too much energy or put a substantial amount of stress on joints and links. This paper proposes a new torque distribution method for reducing the maximum torque of the actuator of a planar PKM. Here the main idea behind the proposed method is the use of superposition of a particular solution for a non-redundant case and an optimized null-space solution for a redundant case with a constant coefficient. The optimal value of a null-space solution can be easily determined by checking only the intersection points of the profile of the actuator's torque as the coefficient varies. We consider three cases of planar PKMs-2-, 3-, and 4-RRR PKMs-and present a detailed procedure for deriving a kinematic solution for the 2-RRR PKM based on Screw theory. We compare the proposed method with the minimum-norm pseudo-inverse method and assess a limitation of the proposed method. The torque distribution algorithm can be used to determine the number of actuators in an efficient manner and to reduce energy consumption.

Kinematic Sensitivity Analysis and Dimensional Synthesis of a Redundantly Actuated Parallel Robot for Friction Stir Welding

“…In a threedimensional space with coordinate axes of l 1 , l 2 , and l 3 , as shown in Figure 6, the parameter design space can be represented by the shaded area, which is determined by the conditions in Eqs. (23) and (24). Furthermore, the three-dimensional design space can be planarized into a two-dimensional design space [50,51] according to the following equation: Figure 7 presents the distribution of (η r , η p , σ r , σ p ) in the parameter design space.…”

“…Wang et al [22] presented the design of an actuation device that could automatically distribute external loads based on stability theorems. Choi et al [23] proposed an optimization method for torque distribution of redundantly actuated planar parallel mechanisms based on a null-space solution. Cheng et al [24] proposed a simple scheme for computing the inverse dynamics of a redundantly actuated parallel manipulator and four basic control algorithms.…”

Stiffness synthesis of 3-DOF planar 3RPR parallel mechanisms

“…According to the Cauchy-Bunyakovsky-Schwarz inequality, k 11 k 22 − k 2 12 ≥ 0 is always true. But as shown in Eq.…”

“…The displacement and the force applied on the end-effector are connected by the stiffness matrix. 1,2 Force control is achieved by adjusting the displacement of the end-effector. For a 3RPR planar parallel robot, the stiffness matrix is generally coupled.…”

Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use

“…On the other hand, redundancy is introduced to improve the kinematic and dynamic behaviors of PMs. [20][21][22][23][24] There are two types of redundancy: kinematic redundancy and actuator redundancy. For the kinematic redundancy, an extra leg is added to the parallel structure and an extra actuator is placed on the base.…”