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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

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Front. Mech. Eng.    2014, Vol. 9 Issue (3) : 233-241    https://doi.org/10.1007/s11465-014-0312-z
RESEARCH ARTICLE
Stiffness of a 3-degree of freedom translational parallel kinematic machine
S. SHANKAR GANESH(),A.B. KOTESWARA RAO
Department of Mechanical Engineering Gayatri Vidya Parishad College of Engineering, Visakhapatnam 530048, India
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Abstract

In this paper, a typical 3-degree of freedom (3-DOF) translational parallel kinematic machine (PKM) is studied and analyzed whose tool platform has only translations along X-, Y- and Z-axes. It consists of three limbs, each of which have arm and forearm with prismatic-revolute-revolute-revolute (PRRR) joints. Inverse kinematics analysis is carried out to find the slider coordinates and joint angles for a given position of tool platform. Stiffness modeling is done based on the compliance matrices of arm and forearm of each limb. Using the stiffness modeling the variations of minimum and maximum translational stiffness in the workspace are analyzed. For various architectural parameters of the 3-DOF PKM the tendency of variations on the minimum and maximum stiffness over the entire workspace is studied; and also the deflections of the tool platform along X, Y, and Z directions with respect to various forces are presented.
Keywords 3-DOF translational PKM      inverse kinematics      stiffness modeling      translational stiffness     
Corresponding Author(s): S. SHANKAR GANESH   
Online First Date: 09 September 2014    Issue Date: 10 October 2014
 Cite this article:   
S. SHANKAR GANESH,A.B. KOTESWARA RAO. Stiffness of a 3-degree of freedom translational parallel kinematic machine[J]. Front. Mech. Eng., 2014, 9(3): 233-241.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0312-z
https://academic.hep.com.cn/fme/EN/Y2014/V9/I3/233
Fig.1  Kinematic sketch of 3-DOF PKM
Fig.2  Schematic diagrams of (a) first limb; (b) second limb; (c) third limb
Fig.3  Auto-Cad model and kinematic sketch of 3-DOF PKM with workspace
Fig.4  Free body diagram of ith limb
ParametersValue
Length of the arm (L1)/m0.681
Length of the arm (L2)/m0.557
Distance of the Z-slider from the origin (D1)/m1.190
Offset of the Z-slider from the X-axis (D2)/m0.257
Starting point of the X-slider(XI)/m0.259
Starting point of the X-slider(YI)/m0.271
Starting point of the X-slider(ZI)/m-0.682
Length of the platform (Lp)/m0.100
Tab.1  Dimensions of the 3 DOF Translational PKM
Fig.5  Variation of minimum and maximum translational stiffness at the (a) Top plane; (b) middle plane; (c) bottom plane
PlaneMinimum of minimum stiffness/(kN·m-1)Maximum of minimum stiffness/(kN·m-1)Minimum of maximum stiffness/(kN·m-1)Maximum of maximumstiffness/(kN·m-1)
Top855.11074.61036.81661.7
Middle790.7931.5918.51661.7
Bottom709.6799.8855.51661.7
Tab.2  Minimum and maximum translational stiffness at the top, middle and bottom plane
Fig.6  Effect of minimum and maximum translational stiffness for various architectural parameters (a) L1; (b) L2; (c) D1; (d) Lp
Fig.7  Variation of deflection for a force 50 N applied at the tool platform in X, Y and Z directions at the middle plane of Z-plane
DirectionDeflection/mm
MinimumMaximum
X-direction0.05370.0632
Y-direction0.05350.0584
Z-direction0.03010.0584
Tab.3  Variation of deflection for a force of 50 N applied to the tool platform in X, Y and Z directions at the Middle plane
Fig.8  Increase of force applied in X, Y and Z directions
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