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General Terminology Related to Parallel Mechanisms

Available also in French

Basic Terminology

Parallel mechanism: Closed-loop mechanism in which the end-effector (mobile platform) is connected to the base by at least two independent kinematic chains.

Similar terms: parallel robot, parallel manipulator, Stewart platform, Gough-Stewart platform, Gough platform, motion platform, in-parallel mechanism, parallel-link mechanism, closed-loop mechanism, Parallel Kinematic Machine (PKM), hexapod.

The use of the above similar terms is to be determined based on the following definitions.

According to the Terminology for the Theory of Machines and Mechanisms defined by IFToMM (1991):

  • Mechanism: System of bodies designed to convert motions of, and forces on, one or several bodies into constrained motions of, and forces on, other bodies.
  • Spherical mechanism: Mechanism in which all points of its links describe paths located on concentric spheres.
  • Machine: Mechanical system that performs a specific task, such as forming of material, and the transference and transformation of motion and force.
  • Robot: Mechanical system under automatic control that performs operations such as handling and automation.
  • Manipulator: Device for gripping and the controlled movement of objects.
  • Kinematic chain: Assemblage of links and joints.

According to ISO 8373, Manipulating industrial robots-Vocabulary (1994):

  • Manipulator: A machine, the mechanism of which usually consists of a series of segments, jointed or sliding relative to one another, for the purpose of grasping and/or moving objects (pieces or tools) usually in several degrees of freedom. It may be controlled by an operator, a programmable electronic controller, or any logic system (for example cam device, wired, etc.).
  • Parallel Robot: A robot whose arms (primary axes) have three concurrent prismatic joints.

Based on the history of parallel mechanisms and on robotics in general:

  • Gough-Stewart platform: 6-DOF parallel mechanism with six identical kinematic chains, composed of a universal joint, a prismatic actuator, and a spherical joint.
  • Parallel Kinematic Machine (PKM): Machine tool based on a parallel mechanism.
  • Hexapod: 1. Six-footed insect. 2. Walking machine with six articulated legs. 3. PKM with six legs.

Fully-parallel mechanism: Parallel mechanism with an n-DOF end-effector connected to the base by n independent kinematic chains, each having a single actuated joint.

Hybrid parallel mechanism: Parallel mechanism with an n-DOF end-effector connected to the base by m (m < n) independent kinematic chains, each having one or more actuated joints.

Orientational parallel mechanism: Parallel mechanism for which all points on the mobile platform describe paths that are located on concentric spheres.

Similar terms: parallel wrist mechanism.

Architecture Designation

Open kinematic chains are usually described by the sequence of their kinematic pairs (joints), where the following notation is used for the kinematic pairs:

  • P: prismatic;
  • R: revolute;
  • U: universal (Hooke's or Cardan joint);
  • S: spherical;

N.B. Generally, U is used to denote a universal (Hooke`s, Cardan) joint. However, since the universal joint is not a kinematic pair, sometimes (RR) is used instead.

To denote that a joint is actuated, the corresponding letter is underlined (i.e., P or R)

Example: The serial kinematic chains of a Gough-Stewart platform are of type UPS.

Consequently, parallel mechanisms with identical kinematic chains are denoted as n-JJJJ where n is the number of kinematic chains, and JJJJ denotes the type of the kinematic chains, with the last letter denoting the kinematic pair at the mobile platform. Since, the information on the type of kinematic chains and the number of actuators is not sufficient for determining the DOF of the parallel mechanism, the latter should be explicitly stated.


  • The Gough-Stewart platform is a 6-DOF 6-UPS parallel mechanism.
  • The Agile Eye at Laval University is a 3-DOF 3-RRR spherical parallel mechanism.
  • The Tripteron at Laval University is a 3-DOF 3-PRRR parallel mechanism.

Copyright © 2000—2007 by Ilian Bonev Last Update: February 26, 2007