Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

doi:10.1007/s11465-014-0300-3

Front. Mech. Eng.

2014, Vol. 9

Issue (2) : 120-129 https://doi.org/10.1007/s11465-014-0300-3

RESEARCH ARTICLE

Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

S. SHANKAR GANESH(

),A. B. KOTESWARA RAO

Department of Mechanical Engineering, G.V.P. College of Engineering, Visakhapatnam 530048, India

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Abstract

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kinematic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z- axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. Error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.

Keywords translational Parallel Kinematic Machine error modeling global error transformation index

Corresponding Author(s): S. SHANKAR GANESH

Issue Date: 22 May 2014

Cite this article:

S. SHANKAR GANESH,A. B. KOTESWARA RAO. Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine[J]. Front. Mech. Eng., 2014, 9(2): 120-129.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0300-3
https://academic.hep.com.cn/fme/EN/Y2014/V9/I2/120

Fig.1 Kinematic sketch of 3-DOF PKM

Fig.2 Schematic diagrams of (a) first limb, (b) second limb, and (c) third limb

Tab.1 Variables considered for optimization

Tab.2 Errors considered in links and joints

Fig.3 Variation of pose errors along X-direction in the central horizontal plane. (a) When the dimensional and joint errors do not exist; (b), (c), and (d) when the dimensional and joint errors exist and Y-slider at various positions, namely, start point, mid-point, and end point, respectively

Fig.4 Variation of pose errors along Y-direction in the central horizontal plane. (a) When the dimensional and joint errors do not exist; (b), (c), and (d) when the dimensional and joint errors exist and X-slider at various positions, namely, start point, mid-point, and end point, respectively

Tab.3 Optimal solutions and the corresponding design variables

Tab.4 Best solution and the corresponding design variables

Tab.5 Reciprocal of condition number of ETM and its corresponding maximum pose error

Fig.5 Variation of reciprocal of the condition number of the error transmission matrix in the (a) top plane (b) central plane and (c) bottom plane of the workspace for the PKM

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