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RESEARCH PAPERS

# Dynamic Analysis and Counterweight Optimization of the 2-DOF Parallel Manipulator of a Hybrid Machine Tool

[+] Author and Article Information
Jun Wu1

Institute of Manufacturing Engineering, Department of Precision Instruments, Tsinghua University, Beijing 100084, People’s Republic of Chinawu-j03@mails.tsinghua.edu.cn

Jinsong Wang, Liping Wang, Tiemin Li, Yue Liu

Institute of Manufacturing Engineering, Department of Precision Instruments, Tsinghua University, Beijing 100084, People’s Republic of China

1

Corresponding author.

J. Comput. Nonlinear Dynam 2(4), 344-350 (Apr 30, 2007) (7 pages) doi:10.1115/1.2756071 History: Received October 08, 2006; Revised April 30, 2007

## Abstract

This paper focuses on the dynamic modeling and counterweight optimization of the two degree of freedom planar parallel manipulator, which is a subpart of a hybrid machine tool. Based on a kinematic analysis, the dynamic equation is derived by using the Newton-Euler approach. Then, three counterweight modes are presented for the parallel manipulator. According to the cutting force model and motion planning of the cutting tool, the dynamic simulations with three counterweight modes are performed, and the mass of counterweight in each counterweight mode is optimized by minimizing the sum of mean square values of actuator forces. The simulations show that the optimal mass of counterweights does not equal the total mass of moving parts of the parallel manipulator, and each counterweight mode has its advantage and disadvantage. Considering the ease in which a counterweight can be implemented, the counterweight mode where two counterweights are connected to two sliders is adopted for the parallel manipulator.

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## Figures

Figure 1

Three-dimensional model of the hybrid machine tool

Figure 2

The kinematic model

Figure 3

Cutting force in the face-milling process

Figure 4

Relationship between f(p) and p in counterweight mode 1

Figure 5

Driving forces in counterweight mode 1 when p=0.87

Figure 6

Relationship between f(p) and p in counterweight mode 2

Figure 7

Driving forces in counterweight mode 2 and p=0.78

Figure 8

Relationship between f(p1) and p1 in counterweight mode 3

Figure 9

Driving forces in counterweight mode 3 and p1=0.55

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