Kinematic analysis and optimum design of a novel 2PUR-2RPU parallel robot

Abstract

A three-dof 2PUR-2RPU redundantly-actuated parallel-kinematics machine, designed for the machining of complex curved surfaces that require high-speed and high-precision, is the object of study in this paper. The lower-mobility PKM, consisting of two pairs of symmetric, limited-dof limbs, has the advantages of high stiffness, simple kinematic chain, and reduced singularities. The mobility of the robot is investigated via Lie-groups, instead of the well-known Chebyshev–Grübler–Kutzbach formulas, which are not applicable to our case. Then, the inverse-displacement, direct-displacement and corresponding velocity relations are analyzed in detail. Next, by investigating the rank-deficiency of the corresponding Jacobian, three types of singularities, those associated with direct-kinematics, inverse-kinematics and combinations thereof, are analyzed in depth, while constraint singularities are investigated by resorting to constraint wrenches. Moreover, the workspace of both the reference point P and the tool head, when a tool is added to the moving platform, are derived. It is noteworthy that the local and global dexterity indices are evaluated by resorting to the characteristic length to homogenize the dimensionally inhomogeneous Jacobian matrix at hand, then the condition number is minimized over the independent posture parameters and the characteristic length via the first-order normality conditions.