Synthesis of Planar Parallel Mechanisms While Considering Workspace, Dexterity, Stiffness and Singularity Avoidance

Abstract

It is a generally well-known fact that the design of parallel mechanisms while optimizing performance is quite difficult. In this paper, a reliable synthesis method capable of optimally selecting the geometrical parameters of planar parallel mechanisms is presented. Three different architectures are considered and a genetic algorithm is used to perform the optimization. The performance of each mechanism is evaluated according to four different criteria: workspace, singular configurations, dexterity, and stiffness. In order to make the synthesis method as realistic as possible, mechanical constraints affecting the angular rotation of the 2-RPR and 3-RPR mechanisms' passive revolute joints are considered. Moreover, since the conventional methods for computing the dexterity and the stiffness index are not valid for the 3-RPR and 3-RRR mechanisms, an alternative computation method is used.

Inverse dynamics and robust sliding mode control of a planar parallel (2-PRP and 1-PPR) robot augmented with a nonlinear disturbance observer

“…The experiment results along with detailed comparisons are presented in Figs. [17][18][19][20]. The trajectories of the end-effector positions (refer Fig.…”

“…Therefore, from Eqs. (17) and (21), it is observed that the Lyapunov's candidate function is positive definite and its time derivative is negative definite in the entire state space. i.e.,…”

“…Few of the commercially available and research planar parallel robotic platforms are presented in Fig. 1 [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…These platforms have great potentials and advantages for material handling, processing and micro fabrication tasks, because the motions between components are in parallel planes and they are connected by simple joints [3,6]. The detailed kinematic, workspace and singularity analyses of different 3-DOF planar parallel manipulators were investigated and its summary can be found in literature [3,[6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A number of configurations have been proposed (by varying the configuration of the 3-DOF leg) namely 3-RRR, 3-PRR, 3-PPR, 3-PRP, 3-RRP, 3-RPP, and combinations of these legs (PRP + PPR + RRR, etc.)…”

Stiffness modeling of a family of 6-DoF parallel mechanisms with three limbs based on screw theory

“…have to be considered. The global stiffness and workspace of the parallel mechanisms vary with the configuration of the assembled parallel kinematic chains [1][2][3]. In fact, there is always a tradeoff between stiffness and workspace in the design of such mechanisms.…”