Reconfigurability Analysis of a Class of Parallel Kinematics Machines

A novel parallel kinematics machine (PKM) stemming from the 3-SRU (spherical-revolute-universal) under-actuated joints topology is presented in this paper. The concept here proposed takes advantage of a reconfigurable universal joint obtained by locking, one at a time, different rotations of a spherical pair. Such local reconfiguration causes a slight, yet crucial, modification of the robot legs mobility which is enough to provide the end-effector with different kinds of motion. In particular, the kinematic chain is converted to two different 3-URU architectures (universal-spherical-universal) able to provide the moving platform with essentially different mobilities. The paper is dedicated at formally demonstrating the motion capabilities offered by such parallel architectures. To this aim, the first part of the paper describes the mechanical structures and formalizes the kinematic problem through appropriate sets of polynomial equations. Then, an analysis of the equations is proposed to uniquely identify the mobilities of the moving platform. At last, a concept design is proposed for the reconfigurable spherical platform.

Kinematics Analysis of a Class of Spherical PKMs by Projective Angles

This paper presents the kinematics analysis of a class of spherical PKMs Parallel Kinematics Machines exploiting a novel approach. The analysis takes advantage of the properties of the projective angles, which are a set of angular conventions of which their properties have only recently been presented. Direct, inverse kinematics and singular configurations are discussed. The analysis, which results in the solution of easy equations, is developed at position, velocity and acceleration level.

Full-Mobility Three-CCC Parallel-Kinematics Machines: Kinematics and Isotropic Design

The subject of this paper is twofold: the kinematics and the isotropic design of six degrees-of-freedom (DOF), three-CCC parallel-kinematics machines (PKMs). Upon proper embodiment and dimensioning, the PKMs discussed here, with all actuators mounted on the base, exhibit interesting features, not found elsewhere. One is the existence of an isotropy locus, as opposed to isolated isotropy points in the workspace, thereby guaranteeing the accuracy and the homogeneity of the motion of the moving platform (MP) along different directions within a significantly large region of their workspace. The conditions leading to such a locus are discussed in depth; several typical isotropic designs are brought to the limelight. Moreover, the kinematic analysis shows that rotation and translation of the MP are decoupled, which greatly simplifies not only the kinetostatic analysis but also, most importantly, their control. Moreover, it is shown that the singularity loci of this class of mechanism are determined only by the orientation of their MP, which also simplifies locus evaluation and eases its representation.

A Calibration Approach for the Parallel Kinematics Machines Tools Based on Error Sensitivity Analysis

In order to identify the geometrical parameters of parallel kinematics machines tools (PKM), a new parameters identification method is presented. The identification method is proposed based on a pose discrepancy model, which is deduced from the error between the nominal and measurement relative distance of two different spatial locations of the moving platform. In the identification method, an error sensitivity matrix, which expresses the sensitivity between the pose error and geometrical structural parameters error of PKM, can be created with numerical methods. The results of different numerical methods are analyzed. A measurement method to get the precise lengths of legs is presented, which decrease the number of identified parameters. In an experiment, the error of PKM is reduced from 6.71mm to 1.144mm. Therefore, the identification method is verified effective and feasible.

On the terminology and geometric aspects of redundant parallel manipulators

SUMMARYParallel kinematics machines (PKMs) can exhibit kinematics as well as actuation redundancy. While the meaning of kinematic redundancy has been already clarified for serial manipulators, actuation redundancy, which is only possible in PKMs, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM, a nonlinear control system is introduced whose dynamics evolves on c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKMs are classified as full-actuated and underactuated machines. Relating this DOA to degree of freedom allows to classify the actuation redundancy.