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.

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 Optimum Seeking of Redundant Actuators for M-RCM 3-UPU Parallel Mechanism

2020 ◽  
Author(s):  
Chen Zhao ◽  
Jingke Song ◽  
Xuechan Chen ◽  
Ziming Chen ◽  
Huafeng Ding
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Universal Joint ◽  
Prismatic Joint ◽  
Transmission Index ◽  
Redundant Actuators ◽  
Force Transmissibility ◽  
Singular Configuration

Abstract This paper focuses on a 2R1T 3-UPU (U for universal joint and P for prismatic joint) parallel mechanism (PM) with two rotational and one translational (2R1T) degrees of freedom (DOFs) and the ability of multiple remote centers of motion (M-RCM). The singularity analysis based on the indexes of motion/force transmissibility and constraint shows that this PM has transmission singularity, constraint singularity, mixed singularity and limb singularity. To solve these singularproblems, the quantifiable redundancy transmission index (RTI) and the redundancy constraint index (RCI) are proposed for optimum seeking of redundant actuators for this PM. Then the appropriate redundant actuators are selected and the working scheme for redundant actuators near the corresponding singular configuration are given to help the PM go through the singularity.

Design and Experimental Investigation of a New 2R1T Overconstrained Parallel Kinematic Machine With Actuation Redundancy

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Lingmin Xu ◽  
Xinxue Chai ◽  
Qinchuan Li ◽  
Liangan Zhang ◽  
Wei Ye
Keyword(s):  
Inverse Kinematics ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Curved Surfaces ◽  
Parallel Kinematic Machine ◽  
Actuation Redundancy ◽  
Dimensional Parameters ◽  
Force Transmissibility ◽  
Parallel Kinematic

Two rotations and one translation (2R1T) parallel kinematic machines (PKMs) are suitable for the machining of complex curved surfaces, which requires high speed and precision. To further improve rigidity, precision, and avoid singularity, actuation redundancy, and overconstrained PKMs with fixed actuators and limited-degrees of freedom (DOF) limbs are preferred. However, there are few 2R1T PKMs with these features. This paper introduces a new 2R1T overconstrained PKM with actuation redundancy, which is called Tex4. The Tex4 PKM consists of four limited-DOF limbs; that is, two PUR limbs and two 2PRU limbs (where P denotes an actuated prismatic joint, U denotes a universal joint, and R denotes a revolute joint). The kinematic model of the proposed 2PUR-2PRU machine is presented along with the results of mobility, inverse kinematics, and velocity analysis. By considering the motion/force transmissibility, the dimensional parameters of the Tex4 PKM were optimized to obtain an improved satisfactory transmission workspace without singular configurations. Finally, a prototype based on the optimized parameters was fabricated, and its feasibility and accuracy were validated by motion and position error experiments. The Tex4 PKM has the advantages of high rigidity, simple kinematic model, and zero singularity in the workspace, which suggests that it has potential for use in the high-speed machining of curved surfaces.

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.

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.

Mobility, Kinematic Analysis, and Dimensional Optimization of New Three-Degrees-of-Freedom Parallel Manipulator With Actuation Redundancy

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Lingmin Xu ◽  
Qinchuan Li ◽  
Ningbin Zhang ◽  
Qiaohong Chen
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Force Transmission ◽  
Transmission Index ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Force Transmissibility ◽  
Solution Velocity ◽  
Three Degrees Of Freedom

Parallel manipulators (PMs) with redundant actuation are attracting increasing research interest because they have demonstrated improved stiffness and fewer singularities. This paper proposes a new redundantly actuated parallel manipulator that has three degrees-of-freedom (DOFs) and four limbs. The proposed manipulator is a 2UPR-2PRU parallel manipulator (where P represents an actuated prismatic joint, R represents a revolute joint, and U represents a universal joint) that is actuated using four prismatic joints; two of these joints are mounted on the base to reduce the movable mass. Mobility analysis shows that the moving platform has two rotational DOFs and one translational DOF. First, the inverse displacement solution, velocity, and singularity analyses are discussed. Next, the local transmission index (LTI) and the good transmission workspace are used to evaluate the motion/force transmissibility of the 2UPR-2PRU parallel manipulator. Finally, the parameter-finiteness normalization method (PFNM) is used to produce an optimal design that considers the good transmission workspace. It is thus shown that the motion/force transmission of the proposed manipulator is improved by optimizing the link parameters.

A non-overconstrained variant of the Agile Eye with a special decoupled kinematics

Robotica ◽  
2013 ◽  
Vol 32 (6) ◽  
pp. 889-905 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai ◽  
Giovanni Legnani
Keyword(s):  
Angular Displacement ◽  
Universal Joint ◽  
Special Configuration ◽  
End Effector ◽  
Revolute Joint ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Decoupled Motion ◽  
Orientation Mechanism ◽  
Actuated Joints

SUMMARYA non-overconstrained three-DOF parallel orientation mechanism that is kinematically equivalent to the Agile Eye is presented in this paper. The output link (end-effector) of the mechanism is connected to the base by one spherical joint and by another three identical legs. Each leg comprises of, in turns from base, a revolute joint, a universal joint, and three prismatic joints. The three lower revolute joints are active joints, while all other joints are passive ones. Based on a special configuration, some three projective angles of the end-effector coordinates are fully decoupled with respect to the input actuated joints, that is, by actuating any revolute joint the end-effector rotates in such a way that the corresponding projective angle changes with the same angular displacement. The fully decoupled motion is analyzed geometrically and proved theoretically. Besides, the inverse and direct kinematics solutions of the mechanism are provided based on the geometric reasoning and theoretical proof.

scholarly journals A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

2019 ◽  
Vol 9 (24) ◽  
pp. 5461
Author(s):  
Yuhan Chen ◽  
Xiao Luo ◽  
Baoling Han ◽  
Yan Jia ◽  
Guanhao Liang ◽  
...  
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Inverse Kinematics ◽  
Optimization Problem ◽  
Robot Manipulators ◽  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method ◽  
Prismatic Joints ◽  
Cyclic Coordinate Descent

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.

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.

Inverse Kinematics for Planar Parallel Manipulators

1997 ◽  
Author(s):  
Robert L. Williams ◽  
Brett H. Shelley
Keyword(s):  
Inverse Kinematics ◽  
Broad Class ◽  
Parallel Manipulators ◽  
End Effector ◽  
Serial Chain ◽  
Prismatic Joints ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Serial Chains ◽  
Planar Parallel Manipulators

Abstract This paper presents algebraic inverse position and velocity kinematics solutions for a broad class of three degree-of-freedom planar in-parallel-actuated manipulators. Given an end-effector pose and rate, all active and passive joint values and rates are calculated independently for each serial chain connecting the ground link to the end-effector link. The solutions are independent of joint actuation. Seven serial chains consisting of revolute and prismatic joints are identified and their inverse solutions presented. To reduce computations, inverse Jacobian matrices for overall manipulators are derived to give only actuated joint rates. This matrix yields conditions for invalid actuation schemes. Simulation examples are given.

Sign in / Sign up

Export Citation Format

Share Document