Kinematic and Dynamic Analysis of the Gantry-tau, a 3-DoF Translational Parallel Manipulator

The Gantry-Tau is a family of parallel manipulators with three linear actuators. This mechanism is of interest for various applications because of the large workspace and its performance in terms of high acceleration, precision, and stiffness characteristics. This paper presents workspace analysis and calibration for a Gantry-Tau mechanism using its forward kinematics. The mathematical model of the systematic errors in the kinematics model of the manipulator is obtained. Analysis of the error is then performed to identify the parameters that have a dominant effect on the kinematics error and the regions of the workspace with a high error due to the calibration. Minimization of the mean square and mean absolute errors is employed for calibration through kinematics parameters. For demonstration purposes, a SimMechanics kinematic model of the mechanism is used and its calibration is performed over many sampled positions within the workspace borders of the robot. The result demonstrates that the kinematic error is significantly reduced after the calibration.

Performance Evaluation and Calibration of Gantry-Tau Parallel Mechanism

. This extensive review paper, which involves 204 papers,
discusses comprehensively a number of performance indices that are
instrumental in the design of parallel kinematics manipulators. These
indices measure the workspace as well as its quality including the distance
to singularity, dexterity, manipulability, force transmission, accuracy,
stiffness, and dynamic performance. After being classified, the indices are
discussed in terms of some important aspects including definition, physical
meaning soundness, dependency, consistency, scope of applicability, and
computation cost. For the sake of completeness, some key mathematical
expressions of the indices are provided.

/pdf/review-article-performance-measures-of-parallel-kinematics-3wcest16eb.pdf

Review article: Performance measures of parallel kinematics manipulators

Kinematic and dynamic analysis of a novel parallel kinematic Schönflies motion generator

Compliance model of Exechon manipulators with an offset wrist

Configuration and singularity analysis of a parallel hip joint simulator based on the forward kinematics

An integrated stiffness model is established for a Planar Parallel Manipulator (PPM) with actuation redundancy based on Finite Element Method (FEM), and the static stiffness, dynamitic stiffness and moving stiffness of the PPM are analyzed according to the integrated stiffness model. Firstly, a dynamic model of flexible plane beam element is created as a basic unit for branches. Secondly, each branch is assembled in generalized coordinates, and the integrated stiffness model of the PPM is established. Then calculation and simulation for the static stiffness, dynamitic stiffness and moving stiffness are carried out. The results show that the static stiffness and dynamitic stiffness are related with the position and posture of the PPM. The moving stiffness shows that the elastic deformations cause the oscillation of the PPM. In this paper, three stiffness models are unified in the integrated stiffness model, which improves the efficiency of the stiffness calculation and mechanism design.

/pdf/integrated-stiffness-analysis-of-redundant-parallel-30s03f29ha.pdf

Gang Cheng

Papers

Configuration and singularity analysis of a parallel hip joint simulator based on the forward kinematics

Integrated Stiffness Analysis of Redundant Parallel Manipulator Based on Finite Element Method