Six-Dimensional space expression of workspace of six-DoF parallel manipulators using hyper spherical coordinates (HSC)

A closed-form formulation for the workspace of N-Degrees-of-Freedom (DoF) parallel mechanisms is presented using least-square curve fitting. The concepts of multi-dimensional polynomial (MDP) and in hyper spherical coordinates (HSC) are introduced. The boundary of workspaces of those parallel linkag...

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Bibliographic Details
Published in:Advanced robotics 2015-12, Vol.29 (23), p.1527-1537
Main Authors: Mahmoodi, Ali, Sayadi, Amir
Format: Article
Language:English
Subjects:
Boundaries
Exact solutions
hexapod
hyper spherical coordinates
Mathematical analysis
parallel manipulator
Polynomials
Singularities
Spherical coordinates
Stewart platform
Trigonometric functions
Voids
workspace
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Description
Summary:A closed-form formulation for the workspace of N-Degrees-of-Freedom (DoF) parallel mechanisms is presented using least-square curve fitting. The concepts of multi-dimensional polynomial (MDP) and in hyper spherical coordinates (HSC) are introduced. The boundary of workspaces of those parallel linkages which are surfaces without voids and concavities can be well approximated by the MDPs in the HSC. First, the boundary points are obtained in HSC considering all physical constrains and probable singularities. Then, an MDP with proper order consisting of sine and cosine functions is fitted to those points. The presented method is general and applicable to all DoF. Three case studies of 2, 3, and 6-DoF mechanisms are investigated to demonstrate the effectiveness of the method. Representative figure for graphical abstract: Figure 8.
ISSN:0169-1864
1568-5535
DOI:10.1080/01691864.2015.1076345