Modern Mechanical Engineering

Volume 4, Issue 2 (May 2014)

ISSN Print: 2164-0165   ISSN Online: 2164-0181

Google-based Impact Factor: 1.11  Citations  

Semi-Analytical Approach for Stiffness Estimation of 3-DOF PKM

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DOI: 10.4236/mme.2014.42010    3,376 Downloads   5,306 Views  Citations
Author(s)

ABSTRACT

Due to their advantageous of high stiffness, high speed, large load carrying capacity and complicated surface processing ability, PKMs (Parallel Kinematic Manipulators) have been applied to machine tools. This paper mainly addresses the issue of stiffness formulation of a three-prismatic- revolute-spherical PKM (3-PRS PKM). The manipulators consist of three kinematic limbs of identical topology structure, and each limb is composed of an actuated prismatic-revolute-spherical. In order to build up the stiffness model, kinematics, Jacobian and finite element analysis are also performed as the basis. Main works in this paper can be outlined as follows. By use of approaches of vector, inverse position analysis of 3-PRS PKM is conducted. When the independent position and orientation parameters of the end-effectors are provided, the translational distances of active prismatic joints can be determined. Then with the aid of the wrench and reciprocal screw theory, the overall Jacobian of this manipulator is formulated quickly, and which is a six by six dimensional matrix and can reflect all information about actuation and constraint singularity. After for- mulating the position analysis and Jacobian matrix, the next step is stiffness analysis. Analytical stiffness model, a function of Jacobian matrix and components stiffness matrix, is obtained first using the principle of virtual work. Stiffness model is also a six by six dimensional matrix and can provide the information of actuation and constraint stiffness simultaneously. For the complex geometry shape of some components, it is impossible to know their stiffness distributions with the varying configuration. Therefore, ANSYS technology has to be applied to compute the stiffness coefficients of these components at different configurations. Then, the computed data are used to obtain the stiffness distribution by use of the numerical fitting method. Up to now, the semi-ana- lytical stiffness model of the manipulator is completely formulated and can be applied to estimate the system stiffness of 3-PRS PKM. The model enables the stiffness of a 3-PRS PKM to be quickly estimated. Provided with the geometry parameters and load situation on tool tip, the stiffness of 3-PRS PKM system is estimated based on the stiffness matrix about tool tip which is obtained by transforming the point from the center of circle composed of three S joints to the tool tip. Then, the stiffness of system along x, y and z directions can be solved. In order to testify the correctness, the corresponding stiffness is also obtained by use of FEA software. The stress distribution and fre- quency of system are also gained by solving the FEA model.

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Nigus, H. (2014) Semi-Analytical Approach for Stiffness Estimation of 3-DOF PKM. Modern Mechanical Engineering, 4, 108-118. doi: 10.4236/mme.2014.42010.

Cited by

[1] Stiffness Modeling and Analysis of a 3-DOF Parallel Kinematic Machine
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[2] Kinetostatic modeling and analysis of an Exechon parallel kinematic machine (PKM) module
Chinese Journal of Mechanical Engineering, 2016
[3] Elastodynamic Model-Based Vibration Characteristics Prediction of a Three Prismatic–Revolute–Spherical Parallel Kinematic Machine
Journal of Dynamic Systems, Measurement, and Control, 2016
[4] A modified elasto-dynamic model based static stiffness evaluation for a 3-PRS PKM
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2015
[5] Elastodynamic modeling and joint reaction prediction for 3-PRS PKM
Journal of Central South University, 2015

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