DEXTEROUS WORKSPACE OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

Abstract

In this work, the dexterous workspace of a general geometry 3-PRRR kinematically redundant planar parallel manipulator with six actuated joints, three of which are redundant, is determined. The 3-PRRR manipulator is an adaptation of the 3-RRR manipulator with a redundant prismatic actuator added to each leg. Obtaining the dexterous workspace by discretizing a large area around the manipulator and determining if each point is in the workspace is relatively simple though computationally inefficient. This work proposes a geometrical method to determine the dexterous workspace of a 3-PRRR planar parallel manipulator. With this method, an exact solution of the workspace boundaries is obtained. The geometrical method uses the four-bar mechanism analogy to determine the dexterous workspace. Though the method is applied to a 3-PRRR planar manipulator, it can be readily applied to any n-PRRR planar manipulator, where n is the number of chains.

Optimal Motion Planning of a Planar Parallel Manipulator With Kinematically Redundant Degrees of Freedom

“…Most of the previous works have focused on inverse kinematics, workspace and singularities avoidance of these mechanisms (e.g. [11][12][13][14][15][16][17]). Wong and Gosselin [11] have introduced three new types of kinematically redundant manipulators by adding one degree of freedom in one of the kinematic chains.…”

Lateral reachable workspace of axially symmetric mobile machining hexapod robots

“…The workspace of the 3-RPR has been previously investigated but either they only solve for the numerical solution for the RW [2] or provide a constant orientation workspace [15][16]. The 3-PRRR and 3-DOF mechanisms are other types of planar parallel mechanisms which have been previously studied [17][18][19][20], but their workspace solution is specific to their mechanisms and cannot be generalized to other cases. The workspace solutions of other notable parallel mechanisms also provide numerical solutions to the workspace of their mechanism [21][22][23][24][25][26][27].…”

“…Although a myriad of workspaces for different types of planar mechanisms have been previously investigated [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], to the best knowledge of the authors, as with hexapod robots, there has been no analytical or mathematical closed-form solution to the RW of planar parallel mechanisms where the workspace spans a surface. A direct or closed-form solution is always more favorable due to simplicity and direct calculation.…”