Kinematics Analysis of 6-DOF Parallel Micro-Manipulators with Offset U-Joints: A Case Study

Kinematics Analysis of 6-DOF Parallel Micro-Manipulators with Offset U-Joints: A Case Study

Mohsen Moradi Dalvand (Monash University, Australia) and Bijan Shirinzadeh (Monash University, Australia)
Copyright: © 2012 |Pages: 13
DOI: 10.4018/ijimr.2012010102
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This paper analyses the kinematics of a special 6-DOF parallel micro-manipulator with offset RR-joint configuration. Kinematics equations are derived and numerical methodologies to solve the inverse and forward kinematics are presented. The inverse and forward kinematics of such robots compared with those of 6-UCU parallel robots are more complicated due to the existence of offsets between joints of RR-pairs. The characteristics of RR-pairs used in this manipulator are investigated and kinematics constraints of these offset U-joints are mathematically explained in order to find the best initial guesses for the numerical solution. Both inverse and forward kinematics of the case study 6-DOF parallel micro-manipulator are modelled and computational analyses are performed to numerically verify accuracy and effectiveness of the proposed methodologies.
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1. Introduction

Due to advantages of parallel manipulators over manipulators with serial kinematics chains, they are commonly used in various industrial and research applications. Positioning errors in serial kinematic chains propagate throughout the chain links, while this is not the case in parallel kinematic chains (Tian, Shirinzadeh, Zhang, & Alici, 2009). Furthermore, parallel structures inherently distribute the forces/torques by the actuators providing this class of robots with high bandwidth dynamic characteristics (Alici & Shirinzadeh, 2006). The parallel structure was originally proposed in Gough machine for testing the tires of the airplane (Gough, 1956) and in Stewart machine as a flight simulator (Stewart, 1965). Thereafter, certain parallel architectures with more potential applications in robotics were developed (Hunt & Primrose, 1993). In the past two decades, parallel manipulators have received considerable research attentions and efforts due to the variety of practical applications. General applications of this kinematics configuration include flight simulators (Salcudean, Drexel, Ben-Dov, Taylor, & Lawrence, 1994; Stewart, 1965); shaking tables used to investigate the effects of earthquakes in building structures; support structures for micro/nano-positioning; industrial robots for high speed assembly (Cleary, Brooks, & Hughes, 1993); force and torque sensors (Kerr, 1989); parallel kinematic machines (Zhao, Fang, Li, Xu, & Zhang, 1998); minimally invasive surgery instruments and even entertainment devices (Merlet, 2006). Parallel architectures were widely investigated and utilised in flexure based mechanisms for micro/nano manipulations (Asif & Iqbal, 2011; Liaw, Shirinzadeh, & Smith, 2008b; Tian, Shirinzadeh, & Zhang, 2009) and for frontier applications such as scanning electron microscopy, atomic force microscopy, cell surgery, nano surgery, and micro/nano surface methodology (Li & Xu, 2009; Liaw, Shirinzadeh, & Smith, 2008a; Yi, Chung, Na, Kim, & Suh, 2003). Parallel manipulators have also been developed for large workspace providing macro/micro manipulation capabilities (Alici & Shirinzadeh, 2006; Portman, Sandler, & Zahavi, 2000). Further, parallel micro/nano manipulators may be integrated with parallel macro/micro manipulators through accurate reconfigurable fixturing techniques (Zubir, Shirinzadeh, & Tian, 2009). This will enable large workspace envelope providing coarse to ultra-precision positioning of an end-effector like a surgical tool (Moradi Dalvand & Shirinzadeh, 2011d; Shoham et al., 2003).

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