Figure 1 depicts a mechanical linkage that converts rotational motion about three base joints (A, B, and C) to translational motion of an end effector (D) in three dimensions. The linkage is fully forward- or back-driveable: It can be driven by motors at joints A, B, and C to obtain a desired translation of end effector D, or else it can be driven in translation at end effector D to generate rotations that can be measured (for example, by use of shaft-angle encoders) at joints A, B, and C. Mechanisms based on this one could be particularly useful as compliant robotic manipulators, force-reflecting hand controllers for such manipulators, and manual position-input devices for computers and other systems (see Figure 2).

Figure 1. This Schematic Diagram shows the geometry and basic kinematic features of the linkage.

The linkage is termed "parallel" because of its multiple pathways between end effector and base. In comparison with serial linkages, which have a single pathway between effector and base, parallel linkages typically have greater structural stiffness.

The linkage is composed solely of rigid link members and simple rotary joints arranged in three conjoined kinematic loops. Two of these loops are spherical (i.e., in either loop, all joint axes intersect at a common center point) and include the base joints A, B, and C. The third loop is planar (i.e., all its joint axes are parallel), with one of its links including the end-effector, D.

Figure 2. A Hand Controller based on the design illustrated in Figure 1 could serve as an input device for a variety of systems that operate under manual control.

For the configuration illustrated in Figure 1, the intersection of the axes of joints A, B, and C (the origin of the X-Y-Z frame) forms the center of a spherical work volume within which the end effector can move.

The advantages afforded by this mechanism are the following:

  • Scaleability- The basic design can be scaled down to devices as small as micromanipulators for advanced surgery or up to machines as large as derricks and cranes.
  • Large Work Volume - Unlike other parallel linkages, this linkage features very large reachable work space, approaching that of open-loop serial linkages of similar size.
  • High Stiffness - The inherent stiffness of parallel linkages in general is increased by the use of a minimal number of joints. The high stiffness, in turn, contributes to accuracy in control of the position of the end effector.
  • Negligible Friction and Backlash - These advantages result principally from elimination of cables, belts, gears, pulleys, and/or lead screws to transfer motion between rotary motors and the end effector.
  • Low Inertia and Moving Weight - Requirements for power, force, and structural reinforcement are reduced by eliminating the need to carry large, bulky motors: all motor housings are always fixed to ground.
  • High Force and Power Output - More (relative to typical other mechanisms of similar size) force and power are available for output because less actuator force must be expended to counteract friction losses and/or to support excessive linkage and actuator weight.
  • Fabrication and Assembly - Despite the multiple-loop parallel configuration of this mechanism, there are few alignment prerequisites for successful assembly and operation.

This work was done by Bernard D. Adelstein of Ames Research Center. For further information, access the Technical Support Package (TSP) free on-line at under the Mechanics category.

This invention has been patented by NASA (U.S. Patent No. 5,816,105). Inquiries concerning nonexclusive or exclusive license for its commercial development should be addressed to

the Patent Counsel
Ames Research Center
(650) 604-5104.

Refer to ARC-14066.