On the optimal kinematic design of the PRRRP 2-DoF parallel mechanism

This paper addresses performance analysis and optimum design of a PRRRP parallel mechanism that is actuated vertically by linear actuators. Kinematically, the symmetrical PRRRP parallel mechanism has two geometric parameters, i.e., the link length of each of the two legs and the horizontal distance between two P joints. Unlike the traditional optimum design method used in parallel mechanisms, this paper proposes a design approach utilizing a performance chart, which has been applied to most industrial designs. Here, the indices to evaluate the workspace, control accuracy, velocity, payload capability, and stiffness are defined and investigated. A finite design space, which makes it possible to illustrate the relationships between the indices and parameters, is developed by normalizing the two parameters. The performance charts are then constructed. Such charts are very useful to identify an optimum region, which represents a domain of the normalized parameters, with respect to specified indices. The good-condition workspace (GCW) of a selected mechanism from such an optimum region is used as the basic criterion to determine the dimensional scale D, which is used to normalize the two parameters of the mechanism. The scale is actually the ratio of the desired workspace to the GCW. As the developed finite space contains all possible normalized PRRRP mechanisms and the parameter D determines all of its similarity mechanisms, the design method proposed in this paper can guarantee an optimum result. Since the optimum region is the intersecting result with different performance charts, multi-criteria optimum design is no longer a difficulty. What is more, the method is very convenient for a designer to select an optimum design candidate appropriate to the design condition he faces.