An analytical approach for positioning error and mode shape analysis of n – legged parallel manipulator

ABSTRACT

Precise part positioning on a parallel manipulator is a challenging task for industries where positioning errors can restrict achieving the required quality of the part. However, in the literature, the positioning errors of the parallel manipulator are not explored extensively. In this paper, the main focus was to find out positioning errors of the parallel manipulator caused while machining. Lagrange formulation is used as part of the proposed analytical model to calculate the positioning errors of the platform under external forces. Moreover, the proposed generalised algorithm gives the positioning error of ‘n’ legged manipulator for any initial orientation of the platform, along with, eigenvalues and corresponding eigenvectors of the manipulator. The results are validated with software-based finite element analysis and by solving a numerical study from the literature. This approach can also be used for optimisation of design variables for minimum positioning error of the Gough–Stewart Platform.

KEYWORDS:

• Stewart Platform
• parallel manipulator
• Lagrangian formulation
• 3D trusses
• finite element analysis
• 3D stiffness matrix

Disclosure statement

No potential conflict of interest was reported by the authors.