Optimal Design of a Metamorphic Parallel Mechanism With Reconfigurable 1T2R and 3R Motion Based on Unified Motion/Force Transmissibility

2016 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Optimal Design ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Rotation Axis ◽  
Geometric Constraint ◽  
Transmission Performance ◽  
Trade Off ◽  
Pure Rotation ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism which can switch its motion between one translation and two rotation (1T2R) motion and pure rotation (3R) motion. This feature stems from a reconfigurable revolute (rR) joint of which the rotation axis can be altered freely. Screw based geometric constraint is used to demonstrate the reconfiguration and mobility. Unified inverse kinematics, Jacobian matrix and motion/force transmissibility are provided using screws. Based on those, singularity loci are illustrated and optimal design of some key parameters are conducted considering both the 1T2R and 3R phases. Trade-off can be made between the maximum singularity-free workspace and transmission performance based on the optimal design results in this paper for specific applications requiring 1T2R and 3R motion.

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

2015 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Design Parameters ◽  
Force Transmission ◽  
Pure Rotation ◽  
Rotation Axes ◽  
Potential Applications ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism which can switch its motion between pure translation (3T) and pure rotation (3R) motion. This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraint of the parallel mechanism covering both 3T and 3R motion. Following these screw theory based motion/force transmission equations are obtained and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the metamorphic parallel mechanism. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

Optimal Design of 6-UPU Parallel Mechanism

2011 ◽  
Vol 480-481 ◽  
pp. 1055-1060
Author(s):  
Guang Hua Wu ◽  
Lie Hang Gong ◽  
Xin Wei Ji ◽  
Zhong Jun Wu ◽  
Yong Jun Gai
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Optimal Design ◽  
Objective Function ◽  
Parallel Mechanism ◽  
Design Space ◽  
Jacobian Matrix ◽  
Optimal Model ◽  
The Real ◽  
Universal Joints

The methodology of the optimal design for the 6-UPU parallel mechanism (PM) is presented based on genetic algorithms. The optimal index which expressed by Jacobian matrix of the PM is first deduced. An optimal model is established, in which the kinematic dexterity of a parallel mechanism is considered as the objective function. The design space, the limiting length of the electric actuators and the limit angles of universal joints are taken as constraints. The real-encoding genetic algorithm is applied to the optimal design of a parallel mechanism, which is proved the validity and advantage for the optimal design of a similar mechanism.

New Indices for Optimal Design of Redundantly Actuated Parallel Manipulators

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Qinchuan Li ◽  
Ningbin Zhang ◽  
Feibo Wang
Keyword(s):  
Optimal Design ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Mean Value ◽  
Transmission Performance ◽  
Transmission Index ◽  
Redundantly Actuated ◽  
Lower Mobility ◽  
Six Dof ◽  
Force Transmissibility

Redundantly actuated parallel manipulators (PMs) receive growing interest due to their reduced singularity and enlarged workspace. This paper proposes new indices for optimal design and analysis of redundantly actuated PMs by evaluating their motion/force transmissibility. First, we proposed a method to extract a multi-DOF (degrees-of-freedom) redundantly actuated PM into several subsidiary one-DOF PMs with two or more actuators by locking some actuators in an ergodic manner. Then, a new index of output transmission performance is proposed by investigating the mean value of the instantaneous power produced by the multiple actuation wrenches and one twist of the moving platform of one-DOF PMs. A local transmission index (LTI) is defined as the minimum value of the index of output and input transmission performance. A global transmission index (GTI) is then established based on the LTI. The proposed LTI and GTI are coordinate-free and have clear physical interpretation. Finally, the validity and universality of the new indices are demonstrated by optimization and analysis of redundantly actuated lower-mobility PMs with extra articulated six-DOF or limited-DOF limbs.

Performance Analysis and Optimal Design of a 3-DOF 3-PRUR Parallel Mechanism

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Daxing Zeng ◽  
Zhen Huang ◽  
Wenjuan Lu
Keyword(s):  
Optimal Design ◽  
Performance Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Performance Indices ◽  
Geometrical Characteristics

In this paper, a 3-DOF 3-PRUR parallel mechanism (PM) is chosen for performance analysis and optimal design. First, the mobility of the PM is analyzed by using screw theory. Then, the kinematics of this PM is studied based on the geometrical characteristics and the Jacobian matrix is derived. Furthermore, we research some performance indices with respect to the Jacobian matrix over the whole workspace and nondimensional parameters when the input is given, and their performance atlases are obtained with different inputs. Finally, the optimal design of the PM is determined according to the performance atlases, and some examples are presented.

Kinematics and Singularity Analyses of a 2-RPU&SPR Parallel Manipulator

2013 ◽  
Vol 441 ◽  
pp. 568-571
Author(s):  
Jian Hui Fan ◽  
Bin Li ◽  
Xin Hua Zhao
Keyword(s):  
Numerical Simulations ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Algebraic Method ◽  
Singularity Analysis

In this paper, kinematics and singularity of a 2-RPU&SPR parallel mechanism are analyzed by algebraic method. Firstly, the inverse kinematics of the parallel mechanism is derived. Secondly, the Jacobian matrix of the parallel mechanism is obtained and the singularity of the mechanism is analyzed. Finally, the correctness of singularity analysis of the mechanism is verified by numerical simulations.

Investigation of a novel 2R1T parallel mechanism and construction of its variants

Robotica ◽  
2021 ◽  
pp. 1-15
Author(s):  
Jingfang Liu ◽  
Xiangmeng Fan ◽  
Huafeng Ding
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Rotation Axis ◽  
End Effector ◽  
Parasitic Motion ◽  
Structure Synthesis ◽  
Synthesis Strategy ◽  
Continuous Rotation ◽  
Large Rotations

Abstract A 3-RRPRR variable spherical symmetrical parallel mechanism (PM) with arc-shaped sliding pairs and no parasitic motion is presented, exhibiting two rotational and one translational (2R1T) degrees of freedom. Three limbs are symmetrically distributed between the base and end-effector; upper and lower parts of each limb are mirror symmetrical around the middle. The geometry, mobility, forward/inverse kinematics, workspace, and parasitic motion of the mechanism are analyzed, showing its ability to achieve large rotations around a continuous rotation axis. Finally, a structure synthesis strategy for variable spherical symmetrical PM is proposed, and several limb types meeting the conditions are obtained.

Unified Kinematics Analysis and Analytic Singularity-Free Workspace of a Metamorphic Parallel Mechanism With Controllable Rotation Center

2014 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Coordinate System ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Central Line ◽  
Kinematics Analysis ◽  
Base Plane ◽  
Analytic Singularity ◽  
Rotation Center ◽  
Pure Rotation ◽  
Rotation Motion

This paper presents a metamorphic parallel mechanism with controllable rotation center in its pure rotation topology. Based on reconfiguration of a reconfigurable Hooke (rT) joint, the rotational center of the mechanism can be altered along the central line perpendicular to the base plane. A unified Dixon resultant based method is proposed to solve the forward kinematics analytically by covering all configurations with variable rotation centers while the rotation motion is expressed using Cayley formula. Then singularity loci are derived and represented in a new coordinate system with the three Rodrigues-Hamilton parameters assigned in three perpendicular directions. Limb-actuation singularity loci are also obtained from row vectors of the Jacobian matrix. By using Cayley formula, analytical workspace boundaries are expressed by including the mechanism structure parameters and input actuation limits. Finally, singularity-free workspace of configurations with variable rotation centers is demonstrated in the proposed coordinate system.

Kinematic Analysis of a Three-DOF Parallel Mechanism for Telescope Applications

1997 ◽  
Author(s):  
J. A. Carretero ◽  
M. Nahon ◽  
B. Buckham ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Constraint Equations ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

Abstract This paper presents a kinematic analysis of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described and its forward and inverse kinematics solutions are derived. Because the mechanism has only three degrees of freedom, constraint equations must be generated to describe the inter-relationship between the six Cartesian coordinates which describe the position and orientation of the moving platform. Once these constraints are incorporated into the kinematics model, a constrained Jacobian matrix is obtained. The stiffness and dexterity properties of the mechanism are then determined based on this Jacobian matrix. The mechanism is shown to exhibit desirable properties in the region of its workspace of interest in the telescope focussing application.

The Inverse Kinematics and Simulation of a Novel 3-DOF Parallel Mechanism

2014 ◽  
Vol 694 ◽  
pp. 283-287
Author(s):  
Xiao Lin Dai ◽  
Yi Chen ◽  
Lei Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Geometric Constraint ◽  
Simulation Based

A novel 3-DOF parallel mechanism is presented and the inverse kinematics is derived by using geometric constraint between each rods. The co-simulation based on ADAMS is proceeded to verify the correctness of the inverse kinematics. This algorithm is the basis for the application of such parallel mechanism.

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Force Transmission ◽  
Pure Rotation ◽  
Rotation Axes ◽  
Potential Applications ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism (MPM) which can switch its motion between pure translation (3T) and pure rotation (3R). This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable, and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraints of the parallel mechanism covering both 3T and 3R motion. Following this, screw theory based motion/force transmission equations are obtained, and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the MPM. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

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