Abstract:
In last few decades, parallel manipulators have become an essential tool for many
industries due to their high speed, accuracy, payload, stiffness and precision. These features
make parallel manipulator ideal for jobs like, robotic surgery, precise manufacturing, missile
launching and flight simulation, but precise part positioning on parallel manipulator is a
challenging task in industry. With errors in position, one can never achieve the required quality
of the part. In this work, our main focus is to find out positioning errors of a hexapod platform
that are caused while machining. Legs will be considered elastic while the platform, part and
leg-platform contacts will be considered rigid bodies. All legs are assumed to be 3D massless
elastic trusses. When the load is applied on the part placed on the platform, its position may
change due to elasticity of the manipulator. 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 us the positioning error of “n”
legged system and for any initial orientation of the platform. In the second part, Natural
frequencies of Stewart Platform are calculated from results generated in first part. The proposed
methodology is applied on H-840 Hexapod designed and manufactured by Physik Instrumente.
The Hexapod is designed and modelled in CATIA® and results are validated with Finite
Element Analysis, as well as, from the literature.
