Ilian A. Bonev

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.

Constraint singularities of parallel mechanisms

The concept of constraint singularity is introduced. This is a phenomenon occurring in parallel mechanisms with reduced freedoms when the screw system, formed by the constraint wrenches in all legs, loses rank.

A new approach to orientation workspace analysis of 6-DOF parallel manipulators

This paper presents a new discretization method for the computation of the orientation workspace of 6-DOF parallel manipulators, defined as the set of all attainable orientations of the mobile platform about a fixed point. The method is based on the use of a modified set of Euler angles and a particular representation of the orientation workspace. In addition, a direct method is suggested for the computation of the projected orientation workspace, defined as the set of all possible directions of the approach vector of the mobile platform. Alternative ways of computing these two types of workspaces are also discussed with typical examples.

A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators

This paper presents a geometrical method for the workspace analysis of 6-PRRS parallel manipulators. A geometric algorithm is described for the computation of the constant-orientation workspace, which was implemented in the CAD/CAM system CATIA. The influence of the different design parameters on the workspace, as well as on other properties of the manipulator, is discussed. In addition, a new representation of the mobile platform orientation is presented for easier interpretation of the orientation. Finally, examples are provided to demonstrate the usefulness of the method.

Orientation Capability, Error Analysis, and Dimensional Optimization of Two Articulated Tool Heads With Parallel Kinematics

Because of the increasing demand in industry for A/B-axis tool heads, particularly in thin wall machining applications for structural aluminium aerospace components, the three-degree-of-freedom articulated tool head with parallel kinematics has become very popular. This paper addresses the dimensional optimization of two types of tool head with 3-P V P H S and 3-P V RS parallel kinematics (P, R, and S standing for prismatic, revolute, and spherical joint, respectively; the subscripts V and H indicating that the direction of the P joint is vertical or horizontal, and the joint symbol with underline means the joint is active) by considering their orientation capability and positioning accuracy. We first investigate the tilt angle of the spherical joint, the orientation capability, and the error of one point from the mobile platform caused by input errors. Optimization of the 3-P V P H S tool head is easy. For the 3-P V RS tool head, a design space is developed to illustrate how the orientation capability and error index are related to the link lengths. An optimization process is accordingly presented. Using the optimization method introduced here, it is not difficult to find all the possible optimal solutions.

Working and assembly modes of the agile eye

This paper deals with the in-depth kinematic analysis of a special parallel wrist, called the agile eye. The agile eye is a three-legged spherical parallel robot with revolute joints, in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its workspace is unlimited and flawed only by six singularity curves (instead of surfaces). These curves correspond to self-motions of the mobile platform and of the legs, or to a lockup configuration. This paper also demonstrates that the four solutions to the direct kinematics of the agile eye (assembly modes) have a simple direct relationship with the eight solutions to the inverse kinematics (working modes)

Constraint Singularities as C-Space Singularities

This paper examines the phenomenon of constraint singularity of a parallel mechanism, as defined in a recent publication. We focus our attention on the fact that constraint singularities are always singular points of the configuration space of the kinematic chain. As such, they separate distinct configuration space regions and may allow transitions between dramatically different operation modes. All this is exemplified by a multi-operational parallel mechanism that can undergo a variety of transformations when passing through singular configurations.

A closed-form solution to the direct kinematics of nearly general parallel manipulators with optimally located three linear extra sensors

This paper presents a new closed-form solution of the direct kinematic problem of nearly general parallel manipulators by using three linear extra sensors. The sensors are disposed at optimal location, connecting the planar base and the planar mobile platform at distinct points. The basic idea is to use the coordinates of the three distinct anchor points of the extra sensors on the mobile platform to represent the pose of the mobile platform. Thus, the extra sensory data enable one to reduce the problem to the solution of a system of six linear equations in six of the nine generalized coordinates. The other three coordinates are obtained directly from the extra sensory data. In addition, an optimal location of the extra sensors is sought by minimizing the condition number of the linear equations for the least sensitivity to sensor measurement errors. A numerical example is presented for optimal sensor location and the error behavior of the proposed solution scheme by computer simulation.

Singularity Loci of Spherical Parallel Mechanisms

This paper presents the computation and representation of the Type 2 singularity loci of symmetric spherical parallel mechanisms based on a not-well-known intuitive orientation representation. The latter, previously introduced under the name of the Tilt-and-Torsion angles, is briefly described. Then, to illustrate the approach, the two most basic spherical parallel mechanisms are considered and their Type 2 singularities are fully analyzed for various designs.

A new method for solving the direct kinematics of general 6-6 Stewart Platforms using three linear extra sensors

This paper presents a new method for solving the direct kinematics problem of a general Stewart Platform by using three linear extra sensors. The sensors are disposed at a most general way, connecting the non-planar base and the planar mobile platform at distinct points. The extra sensory data enables to reduce the problem to the solution of an overdetermined system of 6 quadratic equations in 3 unknowns. Random numerical examples have demonstrated the existence of a unique solution to this system.