Abstract
This paper presents a new approach to the velocity and acceleration analyses 3DOF parallel manipulators. Building on the definition of the ‘acceleration motor’, the forward and inverse velocity and acceleration equations are formulated such that the relevant analysis can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3- PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.
Highlights
Lower mobility parallel manipulators having fewer than six degrees of freedom (DOF) continue to draw interest from both industry and academia because they regularly offer improved balance between speed, accuracy, rigidity and reconfigurability when compared with conventional machine tools and industrial robots having serial architectures.Velocity, accuracy, stiffness and rigid body dynamic behaviours are important performance factors that‟s should be considered in the design of lower mobility parallel manipulators
This paper presents a new approach to the velocity and acceleration analyses 3DOF parallel manipulators
Systematic approaches are available for velocity analysis of lower mobility parallel manipulators using either kinematic influence coefficient methods or screw theory based methods (Huang et al, 2000; Joshi & Tsai, 2002; Jhu et al, 2007) it is by no means an easy task to use these approaches for acceleration analysis owing to the nonlinearity arising from the second order partial derivatives
Summary
Lower mobility parallel manipulators having fewer than six degrees of freedom (DOF) continue to draw interest from both industry and academia because they regularly offer improved balance between speed, accuracy, rigidity and reconfigurability when compared with conventional machine tools and industrial robots having serial architectures. Having a goal of achieving a general and compact form of the Hessian matrix, the kinematic influence coefficient method was proposed for dealing with the acceleration analysis of serial manipulators (Thomas & Twsar, 1982). This idea was extended to cover full and lower mobility parallel manipulators (Huang, 1985a; Huang, 1985b; Zhu, 2005; Huang, 2006; Zhu et al, 2007). Drawing primarily on the generalized Jacobian and on the strengths of the kinematic influence coefficient method and the concept of accelerator, we propose a new approach for acceleration analysis of lower mobility parallel manipulators.
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