Abstract
This article focuses on the forward kinematic analysis of a class of asymmetrical parallel manipulators by the proposed elimination approach. To solve the key forward kinematic constraint equations with transcendental parameters of the manipulator, an improved elimination algorithm is presented. First, by analyzing the geometry structure of the manipulator, we find the inherent triangular-topology relations of the manipulator. Further, by utilizing the parameter transformation of angular, the key transcendental equations of forward kinematic analysis are formulated into compact polynomial ones. In this context, comparing with the screw approach by Gallardo-Alvarado suggested that the computation efficiency of our proposed approach is superior. Finally, an example of the asymmetrical variable geometry truss manipulator illustrates the effectiveness of the proposed approach.
Highlights
Forward kinematics is a primary problem for the concept design and analysis of asymmetrical parallel manipulators (PMs)
As a representative of asymmetrical PMs, asymmetrical variable geometry truss (VGT) manipulators have received a great deal of attention due to their inherent advantages over the conventional PMs, and these advantages involved simpler structure, higher stiffness, safer device, and had been gained in potential applications.[1]
The computation efficiency of the latter approach is increased by 16.27% than the former one
Summary
Forward kinematics is a primary problem for the concept design and analysis of asymmetrical parallel manipulators (PMs). The algorithm is of global convergence if a desired initial value is demanded in such an iterative process, and further, a feasible or an interesting solution should be close to the solution of the current expected configuration The purpose of this simulation experiment is to synthetically verify the improvement in computational efficiency using polynomial equations by the proposed elimination algorithm instead of transcendental ones used by Gallardo-Alvarado et al.[19] In our discussion, the forward kinematics of the asymmetrical PM By inspection of the coordinate values referred to as the variable X for the mentioned two approaches, we find that center position vectors Xm (m 1⁄4 1; 2; 3; 4) of the mobile platform for the obtained four solutions by the proposed approach are almost consistent with the numerical results of the corresponding vectors in the study of Gallardo-Alvarado et al.[19] In a similar comparison, the norm orientation !. The scheme may be a feasible one to implement mechanics or dynamics analysis of the manipulator in the future
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