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This paper investigates a symmetrical configuration of a known 3-UPU manipulator having three extensible legs and 3 translational degrees of freedom. The kinematics are expressed with respect to a frame that in aligned with the three legs when they are mutually orthogonal. The resulting kinematic equations are symmetric with respect to the three tool coordinates. It is shown that the manipulator stiffness is much greater with the prismatic joints actuated than with the revolute joints actuated. Design enhancements are described for increasing the degrees of freedom to 4 or 6 and for fixing the motors to the stationary base.