Abstract
The singularity problem brings troubles to the design and application for the parallel mechanism. Currently, redundant actuation is one of the useful methods to solve this singularity problem. However, faced to the numerous joints in a parallel mechanism, how to make a quantitative criterion of seeking the most efficient joints added actuators for letting the mechanism passes through singularity is a necessarily open issue. This paper focuses on a 2R1T 3-UPU (U for universal joint and P for prismatic joint) parallel mechanism (PM) with two rotational and one translational (2R1T) degrees of freedom (DOFs) and the ability of multiple remote centers of motion (M-RCM). The singularity analysis based on the indexes of motion/force transmissibility and constraint shows that this PM has transmission singularity, constraint singularity, mixed singularity and limb singularity. To solve these singular problems, the quantifiable redundancy transmission index (RTI) and the redundancy constraint index (RCI) are proposed for optimum seeking of redundant actuators for this PM. Then the appropriate redundant actuators are selected and the working scheme for redundant actuators near the corresponding singular configuration are given to help the PM passes through the singularity. This research proposes a quantitative criterion to optimum seeking of redundant actuators for the parallel mechanism to solve its singularity.
Highlights
The RCM mechanism, which can rotate around a fixed point far away from the mechanism itself [1], is mostly used in minimally invasive surgery robots at the beginning [2,3,4,5]
This paper focuses on this issue and is organized as follows: Section 2 gives the description of an multiple remote centers of motion (M-RCM) 3-UPU parallel mechanism (PM) and its model of inverse kinematics
Output constraint index (OCI) represents the ratio of instantaneous power between constraint wrench screw (CWS) $Ci and output restricted twist screw (ORTS) S/Oi to its corresponding potential maximum power which can be obtained from the following formula: τi =
Summary
The RCM (remote center of motion) mechanism, which can rotate around a fixed point far away from the mechanism itself [1], is mostly used in minimally invasive surgery robots at the beginning [2,3,4,5]. At this time, the mechanism has multiple remote motion centers on plane m, which can be called M-RCM 3-UPU PM. The constraint wrench screw (CWS) $ci is a line vector provide by the ith UPU limb to the mobile platform. ICI represents the ratio of instantaneous power between CWS $Ci (a line vector for this UPU limb) and RTS $rti (a couple for this UPU limb) to its corresponding potential maximum power which can be obtained from the following formula: εi. OCI represents the ratio of instantaneous power between CWS $Ci (a line vector for this UPU limb) and ORTS S/Oi to its corresponding potential maximum power which can be obtained from the following formula: τi =.
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