Investigation of Singularities and Self-Motions of the 3-UPU Robot
We investigate the singular configurations and self-motion phenomena of the 3-UPU robot. Drawing principally upon tools from line geometry and screw theory, we first derive, as a set of six lines, the 6X6 transformation matrix mapping external wrenches acting on the moving platform to the internal forces/moments of the moving platform’s joints. The closest linear complex to these six governing lines is then obtained. The linear complex’s axis and pitch not only provide additional information and understanding on the type and location of the singularities, but also on the nature of any instantaneous motions arising from manufacturing tolerances and low rigidity. It is found that at the home position of certain 3-UPU architectures, the corresponding lines are contained in two zero-pitch linear complexes, causing an instantaneous two-parameter rotational motion about a line pencil at the intersection point of the 3-UPU’s limbs. In the vicinity of the home position the lines are contained in two close linear complexes, offering a theoretical explanation of the observed sensitivity of this mechanism to manufacturing tolerances.
KeywordsParallel robot 3-UPU singularity self motion line geometry.
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