NASA NTRS2006
A proposed three-degree-of-freedom (tilt/tip/piston) manipulator, suitable for aligning an optical or mechanical component, would offer several advantages over prior such manipulators: Unlike in some other manipulators, no actuator would support the weight of another actuator: All of the actuators would be mounted on a base. Hence, there would be less manipulated weight. The basic geometry of the manipulator would afford mechanical advantage: that is, actuator motions would be larger than the motions they produce in the manipulated object. Mechanical advantage inherently increases the accuracy and resolution of manipulation. Unlike in some other manipulators, it would not be necessary to route power and/or data lines through manipulator joints. The proposed manipulator (see figure) would include three prismatic actuators (T1N1, T2N2, and T3N3) mounted on the base and operating in the same plane. Examples of suitable prismatic actuators include lead-screw mechanisms, linear hydraulic motors, piezoelectric linear drives, inchworm-movement linear stepping motors, and linear flexure drives. The actuators would control the lengths of links R1T1, R2T2, and R3T3. Three spherical joints (P1, P2, and P3) would be located at the corners of an equilateral triangle of side length q on the platform holding the object to be manipulated. Three inextensible limbs (R1P1, R2P2, and R3P3) having length r would connect the spherical joints on the platform to revolute joints (R1, R2, and R3) at the ends of the actuator-controlled links R1T1, R2T2, and R3T3. By varying the lengths of these links, one could control the tilt, tip, and piston coordinates of the platform. Closed-form equations for direct or forward kinematics of the manipulator (given the lengths of the variable links, find the tilt, tip, and piston coordinates) have been derived. The equations of inverse kinematics (find the variable link lengths needed to obtain the desired tilt, tip, and piston coordinates) have also been derived.