Improving the Pose Accuracy of Planar Parallel Robots using Mechanisms of Variable Geometry

Abstract

In comparison to classical serial mechanisms parallel kinematic machines (PKM) provide a higher accuracy, a higher stiffness, and higher dynamic properties. However, parallel robots suffer from the presence of singularities within their workspace (Gosselin & Angeles, 1990). In such configurations the moving platform gains at least one degree of freedom (DOF) and the actuation forces become (in theory) infinite. As a result, the kinematic structure can be damaged or even destroyed. Additionally, several performance indices, e.g. the achievable accuracy, are directly related to the singularity loci (Kotlarski, Abdellatif & Heimann, 2008). The closer the endeffector (EE) is ’located’ to a singularity the higher is the pose error resulting from the influence of active joint errors, e.g. from limited encoder resolution. In order to minimize the singularity loci of parallel mechanisms and to increase their performance, e.g. their achievable accuracy, redundancy can be used (Merlet, 1996). Two redundancy approaches are established for PKM, actuation redundancy and kinematic redundancy (Kock & Schumacher, 1998; Wang & Gosselin, 2004). Actuation redundancy can be realized whether by adding a kinematic chain to the mechanism or by actuating a passive joint. Amongst others, it reduces singular configurations and leads to internal preload that can be controlled in order to prevent backlash (Kock, 2001). However, the control of such mechanisms is a challenging task (Muller, 2005). Furthermore, an additional kinematic chain mostly reduces the total workspace. Therefore, kinematic redundancy is proposed realized by adding at least one actuated joint to one kinematic chain (Cha et al., 2007; Mohamed & Gosselin, 2005). It is well known that the singularity loci as well as the achievable accuracy are greatly affected by the geometrical parameters of a mechanism (Kotlarski, de Nijs, Abdellatif & Heimann, 2009; Merlet & Daney, 2005), and are therefore highly dependent on the mechanism’s actual configuration. In this chapter, as examples, kinematically redundant versions of the well known planar 3RRR and 3RPR mechanisms (Gosselin & Angeles, 1988; Zein et al., 2006) are considered. In each case, an additional prismatic actuator is added to an arbitrary base joint. The introduced mechanisms are denoted as 3(P)RRR and 3(P)RPR. Thanks to the additional prismatic actuator, the inverse displacement problem has an infinite number of solutions (Ebrahimi et al., 2007). Hence, reconfigurations of the mechanisms can be performed selectively in order to avoid singularities and to affect their performance directly (Kotlarski, Do Thanh, Abdellatif & Heimann, 2008). It is important to note that with respect to the work of Arakelian et al. (Arakelian et al., 2008), kinematic redundancy can be used to rather change the geometrical parameters of a mechanism than its basic structure. This can be done at the 19