Kinematics, Dynamics and construction of a planarly actuated parallel robot.

Ronen Ben-Horin 1, Moshe Shoham1 and Shlomo Djerassi 2

1 Department of Mechanical Engineering
Technion - Israel Institute of Technology
Technion City, Haifa 32000, Israel
2 RAFAEL - P.O.Box 2250 Haifa, Israel


Kinematic and dynamic analysis of a parallel robot consisting of three planarly-actuated links, is presented in this paper. Coordinated motion of three planar motors, connected to three fixed-length links, produces a six-degrees-of-freedom motion of an output link. Its extremely simple design along with much larger work volume than the commonly used parallel robots make this high performance-to-simplicity ratio robot very attractive. Experimental model verifies the unique combination of large work volume and high accuracy of this robot.

Introduction :

The kinematic structure of most contemporary robots is an open kinematic chain structure (known also as serial manipulators or anthropomorphic structure). Only relatively few commercial robots are composed of a closed kinematic chain (parallel) structure. However, the increasing interest in parallel robots points to the potential embedded in this structure which has not yet been fully exploited. The advantages of parallel robots as compared to serial ones are:

  • higher payload-to-weight ratio since the payload is carried by several links in parallel
  • higher accuracy due to non-cumulative joint error,
  • higher structural rigidity, since the load is usually carried by several links in parallel and in some structures in compression-traction mode only,
  • location of motors at or close to the base,
  • simpler solution of the inverse kinematics equations.

Conversely, they suffer from smaller work volume, singular configurations and a more complicated direct kinematic solution (which is usually not required for control purposes).

A six degrees-of-freedom parallel manipulator was introduced by Stewart in 1965 [Stewart, 1965] and since then has been commonly known as the "Stewart-platform". (It appears that much earlier versions of parallel manipulators were already studied, see [Merlet, 1994]). Many variants of this structure have since been investigated; most of them are configurations having six linearly actuated links with different combinations of link-platform connections such as 3-3, 3-6, and the more general 6-6 one (see Fig. 1). Examples of different structures of parallel manipulators are given in [Chen and Song, 1992; Hunt, 1983; Innocenti and Parenti-Castelli, 1991,1994; Lin et al., 1990,1992; Pierrot et al., 1991; Waldron et al., 1989]. An atlas of parallel robots was composed by Merlet and can be found in the web site [].

ronen_robots.jpg (28192 bytes)

Fig. 1: Stewart platform type 3-3, 3-6, 6-6

This paper analyses a different type of a parallel manipulator that takes advantage of two-degrees-of-freedom planar motors. Coordinated motion of three such planar motors is converted through a spatial mechanism with fixed length links, into a six-degrees-of- freedom motion of the output link. Such a mechanism has many advantages over the common six extendible links parallel manipulators. It has a much larger work volume, very simple forward and inverse kinematic solutions, and it contains only seven moving parts (including motors) and six joints without any gear trains, cables or other power transmission devices. Thus, this robot is probably the simplest six degrees-of-freedom type robot (both parallel and serial) [Tsai and Tamahshebi, 1993; Ben-Horin and Shoham, 1996].

In this paper the kinematic and dynamic analysis of this robot is presented. The dynamic simulation also compares its performance with the common Stewart platform parallel robot. The experimental model, which to the best of our knowledge is the first one that has been actually built, exhibits the unique combination of accuracy and work volume of this robot type.

The manipulator, shown in Fig. 2, consists of the following components: three links of fixed length having a spherical joint on one end and a revolute joint on the other end, three actuators which move planarly on a stationary platform and a six-degrees-of-freedom output platform.

ronen_robot.jpg (46605 bytes)

Fig. 2: A six-degrees-of-freedom parallel manipulator with three planarly actuated links.

EN00500A.gif (2038 bytes) Movie

Full paper: Kinematics, Dynamics and construction of a planarly actuated parallel robot.