Positioning Errors in Parallel Manipulator

Parallel manipulator is ideal for jobs like, robotic surgery, flight simulation, precise manufacturing and 3D-printing but precise part, or tool, positioning on parallel manipulator is a challenging task. With errors in position, one can never achieve the required quality of the part. In this work, main focus is to find out positioning errors of a hexapod platform - during machining. Legs are elastic while the platform, part and leg-platform contacts are rigid bodies. All legs are assumed to be 3D massless elastic trusses. When machining load is applied on the part placed on the platform, the position of platform may change due to elasticity. Lagrange formulation is used to calculate the positioning error of the platform, as a result of machining forces and torques. A generalized algorithm is established, using Mathematica®, which gives the positioning error of "n" legged system with any initial orientation of the platform. In the second part, Natural frequencies are calculated. The proposed methodology is applied on Physik Instrumente's H-840 Hexapod. The Hexapod is designed and modelled in CATIA® and results are validated with FE Analysis, as well as, from the literature.