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 , 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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e-mail: xyn@ecjtu.jx.cn
e-mail: fengxi@ryerson.ca
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February 2006
Technical Papers
A Real-Time Method for Solving the Forward Kinematics of a Tripod With Fixed-Length Legs
Younan Xu,
Younan Xu
School of Mechanical & Electrical Engineering,
e-mail: xyn@ecjtu.jx.cn
East China Jiaotong University
, Nanchang, Jiangxi 330013 PRC
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Fengfeng Xi
Fengfeng Xi
Department of Aerospace Engineering,
e-mail: fengxi@ryerson.ca
Ryerson University
, Toronto, ON M5B 2K3, Canada
Search for other works by this author on:
Younan Xu
School of Mechanical & Electrical Engineering,
East China Jiaotong University
, Nanchang, Jiangxi 330013 PRCe-mail: xyn@ecjtu.jx.cn
Fengfeng Xi
Department of Aerospace Engineering,
Ryerson University
, Toronto, ON M5B 2K3, Canadae-mail: fengxi@ryerson.ca
J. Manuf. Sci. Eng. Feb 2006, 128(1): 204-212 (9 pages)
Published Online: April 4, 2005
Article history
Received:
April 9, 2004
Revised:
April 4, 2005
Citation
Xu, Y., and Xi, F. (April 4, 2005). "A Real-Time Method for Solving the Forward Kinematics of a Tripod With Fixed-Length Legs." ASME. J. Manuf. Sci. Eng. February 2006; 128(1): 204–212. https://doi.org/10.1115/1.2114928
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