Loop closure theory in deriving linear and simple kinematic model for a 3-DOF parallel micromanipulator

Abstract

Various types of micro-motion devices have been developed in the past decade for applications including the manipulation of cells in micro-surgery and the assembly of micro-chips in micro-assembly industries. Most of the micro-motion devices are designed using the compliant mechanism concept, where the devices gain their motions through deflections. In addition, closed-loop parallel structures are normally adopted due to better stiffness and accuracy compared to the serial structures. However, the forward kinematics of parallel structures are complex and non-linear; to solve these equations, a numerical iteration technique has to be employed. This iteration process will increase computational time, which is highly undesirable. This paper presents a method of deriving a simple, linear and yet effective kinematic model based on the loop closure theory and the concept of the pseudo-rigid-body model. This method is illustrated with a 3 DOF (degree-of-freedom) micro-motion device. The results of this linear method are compared with a full kinematic model for the same micro-motion system. It is proved that the derived kinematic model in this paper is accurate and the methodology proposed is effective. The static model of the micro-motion device will also be presented. The uncoupling property of the micro-motion systems, based on the static model, will be briefly discussed.

Input coupling analysis and optimal design of a 3-DOF compliant micro-positioning stage

“…Yong et al [10] presented a method of deriving a simple, linear kinematic model based on the loop closure theory and the concept of the PRBM. Lin et al [11] approached the dynamic response of flexure-based micro-positioning stages by transforming the infinite degree-of-freedom system into a lumped parameter model with a finite number of degrees of freedom.…”

Modelling and verification of fatigue damage for compliant mechanisms

“…In this section, the loop-closure theory is used to analyse the kinematic behaviours of the compliant mechanism. 25 As shown in Fig. 3, all of the active joints are denoted as A i and passive joints are denoted B i , and C i (i = 1, 2, 3), respectively.…”

“…The PRBM makes it possible to bridge rigid-bodies with flexure bodies. 1 For an RRR mechanism without fatigue damage, the loop-closure theory 25 is applied to develop the kinematic model, and the concept of PRBM is integrated with the Lagrange equation 26 to establish the dynamic model, respectively. For the RRR mechanism with fatigue damage, cracks on flexure hinges are parameterized to evaluate the change of rotational stiffness of circular flexure hinges 24 caused by cracks.…”

Crack Detection Method on Flexure Hinges of 3-RRR Compliant Mechanism

“…Then Yong presented a method of deriving a simple, linear and effective kinematic model based on the PRBM and loop closure theory. The model is proved accurately and the methodology proposed is effective [7].…”