An Explicit Method for Determining the Force-Moment Capabilities of Redundantly Actuated Planar Parallel Manipulators

Abstract

A new explicit methodology for the determination of the force-moment capabilities of nonredundantly and redundantly actuated planar parallel manipulators (PPMs) is presented. This methodology is based on properly adjusting the actuator outputs to their maximum capabilities. As a result, the wrench to be applied or sustained is maximized. For a nonredundantly actuated PPM, one actuator can be maximized, while for a redundantly actuated PPM, one actuator, beyond the one of the nonredundant case, may be maximized for every degree of redundancy added to the mechanism. This methodology is compared to a previous work that required an optimization algorithm. The new method yields more accurate and reliable results and is considerably more efficient. Four studies of force-moment capabilities are considered: maximum force with prescribed moment, maximum applicable force, maximum moment with a prescribed force, and maximum applicable moment. The methodology is used to generate the force-moment capabilities of an existing PPM throughout its workspace.

Task-optimized cable-actuated planar parallel manipulator architecture and its concurrent implementation

“…The concept of a wrench workspace has been studied in [5], [9]- [12], [20], [21]. An interval-based method [13], [15] and a convex-hull method [4], [5], [9], [10] are two current techniques for numerically obtaining the wrench workspace.…”

“…A manipulator which is suited for the task will be able to generate the desired wrenches along that trajectory. The problem of determining the wrenches which can be generated by the PM is computationally expensive; it has been studied by many authors [2], [4], [5], [8]- [11], [13], [15], [20], [21]. A wrench workspace can be numerically obtained to approximate the set of end-effector coordinates inside the reachable workspace which can generate the desired wrenches for a task.…”

The effect of the number of degrees of kinematic redundancy on the actuation forces of a planar parallel manipulator

“…Redundancy has been proposed to reduce or eliminate these singularities. Actuation redundancy (e.g., Merlet 1996;Nokleby et al 2005;Zibil et al 2007) consists of actuating a normally passive joint in one or more branches of the manipulator. Branch redundancy (e.g., Firmani et al 2007;Zhao and Gao 2009;Wu et al 2010) consists of adding an extra actuated branch or branches to a manipulator.…”

Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy

“…It is noted that actuation redundancy does not affect the mobility of a parallel manipulator and only increases the number of actuators [6]. Actuation redundancy can be used to eliminate force-unconstrained configurations [7][8][9] or to satisfy actuator constrains [10,11]. At the same time, it enables the system to modulate the end-effector stiffness by realizing an internal load distribution [12].…”