Manipulator Configurations Based on Rotary-Linear (R-L) Actuators and Their Direct and Inverse Kinematics

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Abstract
In this paper, a new type of two-degree-of-freedom actuator called the rotary-linear (R-L) actuator is described. The R-L actuator permits a rotation and a translation along the axis of rotation, thus simulating a cylinder pair. The R-L actuators are then used in type synthesis of mechanical manipulator chains. Closed-loop three-, four, five, and six-degree-of-freedom chains containing four to nine links, R-L actuators, revolute pairs (R), prismatic pairs (P), cylindrical pairs (C), and spheric pairs (S) are then obtained. A class of manipulator configurations where the hand is connected to the ground via six-degree-of-freedom dyads or triads and containing three grounded R-L actuators is treated for inverse kinematics. Since all the actuators are on the ground in this configuration, higher payload capacities and smaller actuator sizes can be expected from these configurations. In addition, generally, the computations required for inverse kinematics are also significantly less than those required for serial link open-loop manipulators. The direct kinematics, however, is much more involved and computationally intensive for these manipulators than for serial-link manipulators. The direct kinematics of an example manipulator is derived and requires solution of a 16th-order polynomial equation. Numerical examples are presented for illustration.

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