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TECHNICAL PAPERS

A Real-Time Method for Solving the Forward Kinematics of a Tripod With Fixed-Length Legs

[+] Author and Article Information
Younan Xu

School of Mechanical & Electrical Engineering, East China Jiaotong University, Nanchang, Jiangxi 330013 PRCxyn@ecjtu.jx.cn

Fengfeng Xi1

Department of Aerospace Engineering, Ryerson University, Toronto, ON M5B 2K3, Canadafengxi@ryerson.ca

1

Corresponding author who completed this work while visiting the East China Jiaotong University.

J. Manuf. Sci. Eng 128(1), 204-212 (Apr 04, 2005) (9 pages) doi:10.1115/1.2114928 History: Received April 09, 2004; Revised April 04, 2005

This paper presents a real-time method for solving the forward kinematics of a tripod with fixed-length legs. The basic idea is to model the problem at hand based on a spatial four-bar linkage through which three sliding legs can be interrelated by choosing one link as a driving variable and other two links as driven variables. As a result, the original multivariable nonlinear problem with three variables can be reduced to one variable problem. A complete approach is provided to solve the unitary nonlinear programing problem. This includes a method for solving the implicit functions in terms of the driving and driven variables, and an approximation method for selecting an initial value leading to a fast solution. The simulation results show that (i) the method is effective, (ii) can reach very accurate results within five iterations for an error bound of 1010, and (iii) numerically very stable. The experiment results show that the proposed forward kinematic method is fast enough to be implemented in real time to provide an accurate prediction of the tool pose from the joint encoder measurement.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Design model of the hybrid machine and (b) Prototype of the hybrid machine at Ryerson University

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Figure 2

Kinematic model for a tripod with fixed-length legs

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Figure 3

Spatial four-bar linkage model of the tripod

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Figure 4

Relationship between β2 and the pose of MP

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Figure 5

Convergence for computing β2

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Figure 6

Singular configuration for testing

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Figure 7

Results for forward to inverse

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Figure 8

Results for inverse to forward

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Figure 9

Tool path for experiment test

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Figure 10

Test results for the tripod at Ryerson University

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Figure 11

Plane of O−bisipi

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