Stewart Platform is a six degree of freedom, parallel manipulator, which consists of a base platform, a coupler platform and six limbs connected at six distinct points on the base platform and the coupler platform. The forward position analysis problem of Stewart Platform amounts to finding all its possible configurations based on the knowledge of the lengths of its limbs. In this paper, we present a numerical method for solving the forward position analysis problem for the most general Stewart Platform. This is a numerical method based on the polynomial continuation as established in recent works in the literature. However, one main difference is that the start system and the homotopy used here are based on physical design rather than pure mathematical equations. First, the target Stewart Platform is geometrically simplified into a platform, which, as the start platform, can be solved analytically. Then, a homotopy is constructed between the kinematics equations of the start platform and those of the target platform. By changing the parameters of the start platform incrementally into the parameters of the target system while tracking solutions of the start platform, a complete set of 40 solutions to the target platform can be found. Through this process, all of the extraneous paths have been eliminated before the solution tracking procedure starts and only isolated solutions of the start platform are tracked. The process for solutions to switch between real and complex is examined.
Skip Nav Destination
Article navigation
June 2002
Technical Papers
A Real Parameter Continuation Method for Complete Solution of Forward Position Analysis of the General Stewart
Zongliang Mu, PhD Student,
Zongliang Mu, PhD Student
Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139
Search for other works by this author on:
Kazem Kazerounian, Professor, Fellow ASME
Kazem Kazerounian, Professor, Fellow ASME
Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139
Search for other works by this author on:
Zongliang Mu, PhD Student
Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139
Kazem Kazerounian, Professor, Fellow ASME
Mechanical Engineering Department, University of Connecticut, Storrs, CT 06269-3139
Contributed by the Mechanisms & Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 2000. Associate Editor: G. S. Chirikjian.
J. Mech. Des. Jun 2002, 124(2): 236-244 (9 pages)
Published Online: May 16, 2002
Article history
Received:
November 1, 2000
Online:
May 16, 2002
Citation
Mu, Z., and Kazerounian, K. (May 16, 2002). "A Real Parameter Continuation Method for Complete Solution of Forward Position Analysis of the General Stewart ." ASME. J. Mech. Des. June 2002; 124(2): 236–244. https://doi.org/10.1115/1.1446476
Download citation file:
Get Email Alerts
DeepJEB: 3D Deep Learning-Based Synthetic Jet Engine Bracket Dataset
J. Mech. Des (April 2025)
Design and Justice: A Scoping Review in Engineering Design
J. Mech. Des (May 2025)
Related Articles
Forward Kinematics in Polynomial Form of the General Stewart Platform
J. Mech. Des (June,2001)
A Novel Approach in the Direct Kinematics of Stewart Platform Mechanisms with Planar Platforms
J. Mech. Des (January,2006)
A New Polynomial Solution to the Geometric Design Problem of Spatial R-R Robot Manipulators Using the Denavit and Hartenberg Parameters
J. Mech. Des (March,2001)
Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator
J. Mech. Des (March,2007)
Related Proceedings Papers
Related Chapters
Low Energy Transition Curve
International Conference on Software Technology and Engineering, 3rd (ICSTE 2011)
Scalable Video Streaming Multicast of Multiple Groups over Broadband Wireless Networks
International Conference on Computer Engineering and Technology, 3rd (ICCET 2011)
Cyclic Codes over F q + u F q + v F q + u v F q
International Symposium on Information Engineering and Electronic Commerce, 3rd (IEEC 2011)