Clément Gosselin

Singularity analysis of closed-loop kinematic chains

The different kinds of singularities encountered in closed-loop kinematics chains are analyzed. A general classification of these singularities in three main groups, which is based on the properties of the Jacobian matrices of the chain, is described. The identification of the singular configurations is particularly relevant for hard automation modules or robotic devices based on closed kinematic chains, such as linkages and parallel manipulators. Examples are given to illustrate the application of the method to these mechanical systems. >

A Global Performance Index for the Kinematic Optimization of Robotic Manipulators

In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.

Stiffness mapping for parallel manipulators

Mechanical systems containing closed-loop kinematic chains can exhibit special types of singularities that result in a loss of controllability of the element of interest (output link or gripper link). Therefore, it is very important for the designer to be able to predict this type of behavior. The approach used by the author is to establish stiffness or conditioning maps of the workspace of the manipulator. A method for obtaining these maps for planar and spatial parallel manipulators is presented. The maps reveal the existence of zones where the stiffness is not acceptable and also help the designer by providing a more accurate representation of the properties of the manipulator. >

Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator

A study of the kinematic characteristics of a three degree-of-freedom (dof) parallel mechanism is presented. The architecture of the mechanism is comprised of a mobile platform attached to a base through three identical prismatic-revolute-spherical jointed serial linkages. The prismatic joints are considered to be actuated. These prismatic actuators lie on a common plane and have radial directions of action. The mechanisms inverse displacement solution is obtained. Since the mechanism has only 3 dof, constraint equations describing the inter-relationship between the six motion coordinates are derived. These constraints allow the definition of parasitic motions, i.e., motions in the three unspecified motion coordinates. Architecture optimization of the device is undertaken demonstrating that specific values of design variables allow minimization of parasitic motion.

The agile eye: a high-performance three-degree-of-freedom camera-orienting device

This paper presents some results obtained in the development of a three-degree-of-freedom camera-orienting device. The agile eye, as it is referred to, is capable of an orientation workspace larger than that of the human eye. The miniature camera mounted on the end-effector can be pointed within a cone of 140 degrees opening with plus or minus 30 degrees in torsion. The mechanical architecture of the orienting device is based on a spherical three-degree-of-freedom parallel manipulator which leads to high-performance dynamics. A kinematic optimization has been performed in order to determine the dimensional parameters of the prototype which would provide the best overall accuracy. A complete dynamical model of the manipulator has also been derived and programmed, and simulation results have guided the mechanical design. Finally, a prototype has been built and experimented with.<<ETX>>

Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory

This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified.

Simulation and design of underactuated mechanical hands

Abstract The design of underactuated mechanical hands is addressed in this article. The objective of the research is to design a robust mechanical hand capable of performing industrial tasks involving the grasping of a wide variety of objects with large forces. To this end, the taxonomy of the grasps is first reviewed. Then, the principle of underactiation—which leads to shape adaptation of the hands—is introduced and a review of the existing underactuated mechanical hands is provided. Architectures of two-degree-of-freedom underactuated fingers are then proposed and a simulation tool is designed to analyze their behavior. It is shown that underactuation is a very promising avenue when only grasping is required (no manipulation). Simulation results are given and discussed in order to illustrate the usefulness of the simulator and general design guidelines are proposed. Finally, an underactuated finger is selected and this finger is used in the design of a three fingered hand. Grasp—chosen from the taxonomy—which can be performed with this hand are then illustrated. The design presented here demonstrates that the use of underactuation can lead to versatile grasping capabilities with reduced complexity.

Type synthesis of 3-DOF spherical parallel manipulators based on screw theory

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time.

Type synthesis of 3-DOF translational parallel manipulators based on screw theory

A method is proposed for the type synthesis of 3-DOF (degree-of-freedom) translational parallel manipulators (TPMs) based on screw theory. The wrench systems of a translational parallel kinematic chain (TPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of TPMs. The type synthesis of legs for TPKCs, the type synthesis of TPKCs as well as the selection of actuated joints of TPMs are dealt with in sequence. An approach to derive the full-cycle mobility conditions for legs for TPKCs is proposed based on screw theory and the displacement analysis of serial kinematic chains undergoing small joint motions. In addition to the TPKCs proposed in the literature, TPKCs with inactive joints are synthesized. The phenomenon of dependent joint groups in a TPKC is revealed systematically. The validity condition of actuated joints of TPMs is also proposed. Finally, linear TPMs, which are TPMs whose forward displacement analysis can be performed by solving a set of linear equations, are also revealed.

Workspaces of Planar Parallel Manipulators

This paper presents geometrical algorithms for the determination of various workspaces of planar parallel manipulators. Workspaces are defined as regions which can be reached by a reference point C located on the mobile platform. First, the maximal workspace is determined as the region which can be reached by point C with at least one orientation. From the above regions, the inclusive workspace, i.e., the region which can be attained by point C with at least one orientation in a given range, can be obtained. Then, the total orientation workspace, i.e., the region which can be reached by point C with every orientation of the platform in a given range, is determined. Three types of planar parallel manipulators are described and one of them is used to illustrate the algorithms.