Collins, 1992). Landsberger and Sheridan (1985) have designed a cable-driven parallel mechanism. The parallel-drive hydraulic shoulder joint in Hayward et al. (1993) uses actuator redundancy to increase the workspace.

Kinematic Solvability

For serial mechanisms, the forward kinematics (find the end-point position given the joint angles) is easy, but the inverse kinematics (find the joint angles given the end-point position) is hard. The inverse kinematics is complicated unless the mechanism has a special structure: either a spherical joint or a planar pair (Tsai and Morgan, 1985). Almost all industrial robots have these special structures, but some for design convenience do not, such as the Robotics Research Arm, which has been used in teleoperation. Because of fast computers, iterative techniques to solve the nonlinear kinematics can work in real time.

For parallel mechanisms, the reverse is true: inverse kinematics is easy, but forward kinematics is hard (Waldron and Hunt, 1991).


Actuation comprises the force or torque source (henceforth called the actuator) and any transmission element to connect to a joint or link. The actuation is the primary determinant of performance (speed, accuracy, strength). A survey of actuators for robotics is presented by Hollerbach et al. (1992).


For macro motion control, standard actuators are electric, hydraulic, or pneumatic. For smaller robots (human size and less), electric actuators dominate. For larger robots (e.g., cranes), hydraulic actuators dominate.

Electric Motors and Drives Electric actuators are the most convenient, because the power source is an electric plug. For pneumatic or hydraulic systems, air supplies and hydraulic supplies often make them much less easy to install and maintain. Electric actuators, however, are weak relative to their mass; hence payloads are not great.

To amplify motor torque and couple high-rev motors to low-rev joints, nearly all electrical motor drives employ some form of transmission element, primarily gears. Thus nearly all commercial electric robots employ gears of some form. For space applications, the space shuttle RMS employs special high-ratio hollow planetary gears (Wu et al., 1993). These same gears will be employed in the two-armed SPDM (Mack et al., 1991).

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