Screw Theory-Based Motion/Force Transmissibility Analysis of High-Speed Parallel Robots With Articulated Platforms

2020 ◽  
Vol 12 (4) ◽  
Author(s):  
Qizhi Meng ◽  
Fugui Xie ◽  
Xin-Jun Liu ◽  
Yukio Takeda
Keyword(s):  
High Speed ◽  
Screw Theory ◽  
Parallel Robots ◽  
Essential Property ◽  
Performance Indices ◽  
Transmission Index ◽  
Force Transmissibility ◽  
Kinematic Performance ◽  
Insight Into ◽  
Local Transmission

Abstract Motion/force transmissibility is an essential property reflecting the kinematic performance of parallel robots. Research on this performance of the single-platform parallel robots (SPPRs) has long been concerned and studied. In contrast, although many innovations and applications of the high-speed articulated-platform parallel robots (APPRs) have been presented, few studies on their motion/force transmissibility have been reported. This paper deals with the motion/force transmissibility analysis of high-speed parallel robots with articulated platforms. A modified output transmission index (MOTI) for the high-speed parallel robots with articulated platforms is proposed based on a newly defined concept of equivalent transmission wrench screw. Furthermore, by having an insight into the instantaneous relative motion inside the mobile platform, a medial transmission index (MTI) is proposed to evaluate its internal motion/force transmissibility. Based on these foundations, the local transmission index (LTI) is redefined as the minimum value of the input, modified output, and medial transmission indices. Under the framework of the above performance indices, motion/force transmissibility analysis of two typical high-speed articulated-platform parallel robots, i.e., Heli4 and Par4, are presented. The proposed indices are excepted to be applied to the optimal design of high-speed parallel robots with articulated platforms.

Motion/Force Transmissibility Based Performance Evaluation of a 6-DOF Parallel Robot With 2-DOF Active Joints

2018 ◽  
Author(s):  
Bin Mei ◽  
Fugui Xie ◽  
Xin-Jun Liu ◽  
Xuan Luo
Keyword(s):  
Performance Evaluation ◽  
Degrees Of Freedom ◽  
Evaluation Method ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Six Degrees Of Freedom ◽  
Transmission Index ◽  
Force Transmissibility ◽  
Local Transmission ◽  
Active Joints

3-PP(Pa)S robot is a six degrees of freedom (DOFs) parallel mechanism with 2-DOF active planar joint. For the design and application of the 3-PP(Pa)S robot, it is essential to investigate the motion/force transmissibility of the robot. But previous studies of the motion/force transmissibility have mainly focused on the parallel robots with 1-DOF active joints and thus cannot be directly applied to the 3-PP(Pa)S robot. In this paper, input twist subspace, transmission wrench subspace and output twist subspace are investigated to build mathematical models of the twists and wrenches corresponding to the 2-DOF active planar joint. Afterwards, based on the previous established frame of the local transmission index, some extended performance evaluation indices are defined to describe the motion/force transmissibility of the 3-PP(Pa)S robot. On this basis, the singularity and motion/force transmissibility of this mechanism are investigated. The motion/force transmissibility evaluation method is meaningful and applicable for the 3-PP(Pa)S parallel robot with 2-DOF active joints and can be further applied to other mechanisms with multi-DOF active joints.

scholarly journals A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Wei Li ◽  
Jorge Angeles
Keyword(s):  
High Speed ◽  
Screw Theory ◽  
Parallel Robot ◽  
Simple Expression ◽  
Parallel Robots ◽  
Forward Displacement ◽  
Design Variables ◽  
The Subject ◽  
Stewart Gough Platform ◽  
The Given

A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as all three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via discretization. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

Kinematic Analysis and Dimensional Synthesis of a New 2R1T Parallel Kinematic Machine

2018 ◽  
Author(s):  
Lingmin Xu ◽  
Xubiao Zhu ◽  
Wei Ye ◽  
Qinchuan Li ◽  
Qiaohong Chen
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Kinematic Machine ◽  
Dimensional Synthesis ◽  
Transmission Index ◽  
Fixed Base ◽  
Prismatic Joints ◽  
Force Transmissibility ◽  
Parallel Kinematic ◽  
Local Transmission

This paper deals with the kinematic analysis and dimensional synthesis of a new 2R1T (R: rotation, T: translation) parallel kinematic machine (PKM). This is a 2PRU-UPR (P, R, U standing for prismatic, revolute and universal joint, respectively) PKM that is actuated by three actuated prismatic joints, two of which are mounted on the fixed base to reduce the movable mass. Firstly, the mobility and inverse kinematics of the 2PRU-UPR PKM are proposed. And then the motion/force transmissibility is evaluated by the local transmission index and good transmission workspace. Moreover, the singular configurations are obtained according to the motion/force transmissibility. Dimensional synthesis is carried out based on the GTW, and the optimized architectural parameters with good GTW are obtained. Finally, a prototype based on the optimized parameters has been developed, which has great potential in machining workpieces with curved surfaces.

scholarly journals Screw Theory Based Singularity Analysis of Lower-Mobility Parallel Robots considering the Motion/Force Transmissibility and Constrainability

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Xiang Chen ◽  
Xin-Jun Liu ◽  
Fugui Xie
Keyword(s):  
Screw Theory ◽  
Mathematical Problem ◽  
Engineering Application ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Input And Output ◽  
Lower Mobility ◽  
Force Transmissibility ◽  
Output Constraint

Singularity is an inherent characteristic of parallel robots and is also a typical mathematical problem in engineering application. In general, to identify singularity configuration, the singular solution in mathematics should be derived. This work introduces an alternative approach to the singularity identification of lower-mobility parallel robots considering the motion/force transmissibility and constrainability. The theory of screws is used as the mathematic tool to define the transmission and constraint indices of parallel robots. The singularity is hereby classified into four types concerning both input and output members of a parallel robot, that is, input transmission singularity, output transmission singularity, input constraint singularity, and output constraint singularity. Furthermore, we take several typical parallel robots as examples to illustrate the process of singularity analysis. Particularly, the input and output constraint singularities which are firstly proposed in this work are depicted in detail. The results demonstrate that the method can not only identify all possible singular configurations, but also explain their physical meanings. Therefore, the proposed approach is proved to be comprehensible and effective in solving singularity problems in parallel mechanisms.

Conceptual design and dimensional synthesis of a novel parallel mechanism for lower-limb rehabilitation

Robotica ◽  
2018 ◽  
Vol 37 (3) ◽  
pp. 469-480 ◽  
Author(s):  
Hui Wang ◽  
Wen Li ◽  
Haitao Liu ◽  
Jianxin Zhang ◽  
Songtao Liu
Keyword(s):  
Conceptual Design ◽  
Lower Limb ◽  
Parallel Mechanism ◽  
Generalized Jacobian ◽  
Transmission Index ◽  
Redundantly Actuated ◽  
Kinematic Performance ◽  
Limb Rehabilitation ◽  
Local Transmission ◽  
Lower Limb Rehabilitation

SUMMARYThis paper introduces a novel 2R1T parallel manipulator redundantly actuated by pneumatic muscles for lower-limb rehabilitation. First, the conceptual design of the proposed 3-DOF parallel mechanism is presented. Then, the inverse kinematics and the generalized Jacobian analysis are carried out. Based on the generalized Jacobian and the constraint characteristics of the mechanism, the force/motion transmissibility of the redundantly actuated parallel mechanism is investigatedviafour individual cases without actuation redundancy, leading to a suitable local transmission index for the evaluation of kinematic performance of the proposed mechanism. Finally, the design variables are optimized by maximizing the mean value of the local transmission index with the aid of genetic algorithm. The numerical result shows that the proposed parallel mechanism can achieve a good kinematic performance in its task workspace.

A new insight into the duality between serial and parallel non-redundant and redundant manipulators

Robotica ◽  
2001 ◽  
Vol 19 (4) ◽  
pp. 365-370 ◽  
Author(s):  
Florian Gosselin ◽  
Jean-Paul Lallemand
Keyword(s):  
Screw Theory ◽  
Parallel Robots ◽  
Redundant Manipulators ◽  
Serial Robots ◽  
Internal Forces ◽  
Insight Into

This paper describes detailed velocity kinematics and the statics of serial and parallel robots. Without resorting to the screw theory, the duality between these two types of robots is demonstrated. This duality concerns operational speeds of serial robots and operational forces of parallel robots, as well as internal speeds in redundant serial robots and internal forces in redundant parallel robots. This approach allows a deeper understanding of the duality between these two types of robots, particularly when they are redundant.

Design, analysis and optimization of Hex4, a new 2R1T overconstrained parallel manipulator with actuation redundancy

Robotica ◽  
2018 ◽  
Vol 37 (2) ◽  
pp. 358-377 ◽  
Author(s):  
Lingmin Xu ◽  
Genliang Chen ◽  
Wei Ye ◽  
Qinchuan Li
Keyword(s):  
Inverse Kinematics ◽  
Advanced Manufacturing ◽  
Mobility Analysis ◽  
Universal Joint ◽  
Actuation Redundancy ◽  
Transmission Index ◽  
Prismatic Joints ◽  
Good Potential ◽  
Force Transmissibility ◽  
Local Transmission

SUMMARYPMs with two rotations and one translation (2R1T) have been used as skeletons in various advanced manufacturing equipment where high accuracy and stiffness are basic requirements. Considering the advantages of redundant actuation and overconstrained structure, such as reduced singularities and improved stiffness, a new 2R1T overconstrained PM with actuation redundancy, called Hex4, is proposed in this paper. This is a 2-PUR/2-RPU PM (wherePdenotes an actuated prismatic joint, U a universal joint, and R a revolute joint) that is actuated by four prismatic joints. Compared with some existing 2R1T overconstrained PMs with actuation redundancy, the main advantage of the proposed PM is that the heavy motors of two limbs are mounted on the base to reduce the movable mass and improve dynamic response. First, mobility analysis, inverse kinematics, and velocity analysis are presented. Then, the local transmission index and good transmission workspace are used to evaluate the motion/force transmissibility of the Hex4 PM. The variation tendencies of the two indices with different link parameters are investigated. The singularity is then discussed by considering the motion/force transmissibility. Finally, link parameters are optimized to obtain an improved good transmission workspace. It is shown that the proposed PM has a good potential for high precision applications.

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