There are limited parallel robots applicable to three-axis grinding machines due to the restricted reachable workspace originating from multiple kinematic chains with spatial kinematic joints. The parallel robot will gain significant potential in the industry if a larger workspace can be achieved. This research introduces a special relationship between upper triangular matrix and parallel robot structures for the purpose of designing a group of novel parallel robots without spatial kinematic joints. The detailed inverse kinematic solution of the selected parallel manipulator is derived in accordance with its straightforward architecture. Several singularity configurations are found on the basis of the first-order kinematic relation. The translational reachable workspace is close to a triangular prism. The dexterity and stiffness performances based on the Jacobian matrix are explored for the chosen parallel manipulator. Both indices display a downward trend as the mobile platform rises higher.
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