Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot

Robotica ◽  
2012 ◽  
Vol 31 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Yongjie Zhao
Keyword(s):  
Performance Evaluation ◽  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
End Effector ◽  
Transmission Index ◽  
Delta Robot ◽  
Singular Configuration ◽  
Velocity Transmission

SUMMARYPerformance evaluation of a parallel robot is a multicriteria problem. By taking Delta robot as an object of study, this paper presents the kinematic performance evaluation of a three translational degrees-of-freedom parallel robot from the viewpoint of singularity, isotropy, and velocity transmission. It is shown that the determinant of a Jacobian matrix cannot measure the distance from the singular configuration due to the existing inverse kinematic singularity of a Delta robot. The determinants of inverse and direct kinematic Jacobian matrices are adopted for the measurement of distance from the singular configuration based on the theory of numerical linear dependence. The denominator of the Jacobian matrix will be lost in the computation of the condition number when the end-effector is on the centerline of the workspace, so the Delta robot may also be nearly at a singular configuration when the condition number of the Jacobian matrix is equal to 1. The velocity transmission index whose physical meaning is the maximum input angular velocity when the end-effector translates in the unit velocity is presented. The evaluation of singularity, isotropy, and velocity transmission of a Delta robot is investigated by simulation. The velocity transmission index can also be used for the velocity transmission evaluation of a parallel robot with pure rotational degrees-of-freedom based on the principle of similarity. The physical meaning is modified to be the maximum input velocity when the end-effector rotates in the unit angular velocity.

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 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.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Kinematics, Workspace Optimization, and Performance Evaluation of a 3-Leg 6-DOF Robot in RRRS Configuration

2020 ◽  
Author(s):  
Nathan A. Jensen ◽  
Carl A. Nelson
Keyword(s):  
Performance Evaluation ◽  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Inverse Kinematic ◽  
And Performance ◽  
Workspace Optimization ◽  
Optimization And Performance

Abstract Underactuated parallel manipulators that achieve 6 DOF via multiple controllable degrees of freedom per leg are often pursued and reported due to their large workspaces. This benefit comes at a cost to the manipulator’s performance, however. Such manipulators must then be evaluated in order to characterize their kinematics in terms of position and motion. This paper establishes a pair of inverse kinematic solutions for a previously proposed and prototyped 3-leg, 6-DOF parallel robot. These solutions are then used to define the robot’s workspace with experimental validation and to optimize the robot’s geometry for maximum workspace volume. The linear components of the Jacobian are then defined, allowing for analysis of the manipulability of the robot. The full Jacobian is also defined, and singularities are examined throughout the workspace of the robot.

Experimental results for the flexible joint cable-suspended manipulator of ICaSbot

Robotica ◽  
2013 ◽  
Vol 31 (6) ◽  
pp. 887-904 ◽  
Author(s):  
M. H. Korayem ◽  
M. Bamdad ◽  
H. Tourajizadeh ◽  
A. H. Korayem ◽  
R. M. Zehtab ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Experimental Tests ◽  
Parallel Robot ◽  
Joint Space ◽  
End Effector ◽  
Flexible Joint ◽  
Cable Robot ◽  
Six Dof ◽  
And Control ◽  
Computed Torque

SUMMARYIn this paper, design, dynamic, and control of the motors of a spatial cable robot are presented considering flexibility of the joints. End-effector control in order to control all six spatial degrees of freedom (DOFs) of the system and motor control in order to control the joints flexibility are proposed here. Corresponding programing of its operation is done by formulating the kinematics and dynamics and also control of the robot. Considering the existence of gearboxes, flexibility of the joints is modeled in the feed-forward term of its controller to achieve better accuracy. A two sequential closed-loop strategy consisting of proportional derivative (PD) for linear actuators in joint space and computed torque method for nonlinear end-effector in Cartesian space is presented for further accuracy. Flexibility is estimated using modeling and simulation by MATLAB and SimDesigner. A prototype has been built and experimental tests have been done to verify the efficiency of the proposed modeling and controller as well as the effect of flexibility of the joints. The ICaSbot (IUST Cable-Suspended robot) is an under-constrained six-DOF parallel robot actuated by the aid of six suspended cables. An experimental test is conducted for the manufactured flexible joint cable robot of ICaSbot and the outputs of sensors are compared with simulation. The efficiency of the proposed schemes is demonstrated.

Dynamic Trajectory Planning for a Three Degrees-of-Freedom Cable-Driven Parallel Robot Using Quintic B-Splines

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Sen Qian ◽  
Kunlong Bao ◽  
Bin Zi ◽  
W. D. Zhu
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Planning Method ◽  
End Effector ◽  
B Spline ◽  
B Splines ◽  
Pick And Place ◽  
Two Factors ◽  
Three Degrees Of Freedom

Abstract This paper presents a new trajectory planning method based on the improved quintic B-splines curves for a three degrees-of-freedom (3-DOF) cable-driven parallel robot (CDPR). First, the conditions of positive cables’ tension are expressed in terms of the position and acceleration constraints of the end-effector. Then, an improved B-spline curve is introduced, which is employed for generating a pick-and-place path by interpolating a set of given via-points. Meanwhile, by expressing the position and acceleration of the end-effector in terms of the first and second derivatives of the improved B-spline, the cable tension constraints are described in the form of B-spline parameters. According to the properties of the defined pick-and-place path, the proposed motion profile is dominated by two factors: the time taken for the end-effector to pass through all the via-points and the ratio between the nodes of B-spline. The two factors are determined through multi-objective optimization based on the efficiency coefficient method. Finally, experimental results on a 3-DOF CDPR show that the improved B-spline exhibits overall superior behavior in terms of velocity, acceleration, and cables force compared with the traditional B-spline. The validity of the proposed trajectory planning method is proved through the experiments.

Gateway Configuration for Rapid Pick-and-Place Operations of 2-Degrees-of-Freedom Parallel Robots

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Andrea Martin-Parra ◽  
David Rodriguez-Rosa ◽  
Sergio Juarez-Perez ◽  
Guillermo Rubio-Gomez ◽  
Antonio Gonzalez-Rodriguez ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robots ◽  
End Effector ◽  
Joint Coordinates ◽  
Pick And Place ◽  
Low Energy Consumption ◽  
Simulation Results ◽  
The Difference

Abstract This article presents a new assembling for 2 degrees-of-freedom (DOFs) parallel robots for executing rapid pick-and-place operations with low energy consumption. A conventional design of 2-DOF parallel robots is based on five-bar mechanisms. Collisions between links are highly possible, restricting the end-effector workspace and/or increasing the trajectory time to avoid collisions. In this article, an alternative assembling for preventing collisions is presented. This novel assembling allows exploring the difference between the four five-bar mechanism configurations for the same position of the end-effector. Some of these configurations yield to lower time and/or lower energy consumption for the same motorization. First, a dynamic model of the robot has been developed using matlab® and simulink® and validated by comparison with the results obtained by adams® software. A robust cascade PD regulator for controlling joint coordinates has been tuned providing a high accurate end-effector positioning. Finally, simulation results of four configurations are presented for executing controlled maneuvers. The obtained results demonstrate that the conventional configuration is the worst one in terms of trajectory time or energy consumption and, conversely, the best one corresponds to an uncommonly used configuration. A workspace map where all configurations provide faster maneuvers has been obtained in terms of Jacobian matrix and mechanism elbows distance. The results presented here allow designing a rapid manipulator for pick-and-place operations.

A New 4-DOF Fully Parallel Robot With Decoupled Rotation for Five-Axis Micromachining Applications

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Oleksandr Stepanenko ◽  
Ilian A. Bonev ◽  
Dimiter Zlatanov
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Parallel Robot ◽  
Parallel Kinematic Machine ◽  
Constant Length ◽  
End Effector ◽  
Kinematic Models ◽  
Parallel Kinematic ◽  
Linear Actuators ◽  
Five Axis

We present a novel 4-DOF (degrees of freedom) parallel robot designed for five-axis micromachining applications. Two of its five telescoping legs operate simultaneously, thus acting as an extensible parallelogram linkage, and in conjunction with two other legs control the position of the tooltip. The fifth leg controls the tilt of the end-effector (a spindle), while a turntable fixed at the base of the robot controls the swivel of the workpiece. The robot is capable of tilting its end-effector up to 90 deg, for any tooltip position. In this paper, we study the mobility of the new parallel kinematic machine (PKM), describe its inverse and direct kinematic models, then study its singularities, and analyze its workspace. Finally, we propose a potential mechanical design for this PKM utilizing telescopic actuators as well as the procedure for optimizing it. In addition, we discuss the possibility of using constant-length legs and base-mounted linear actuators in order to increase the volume of the workspace.

DeltaBot: A New Cable-Based Ultra High Speed Robot

2003 ◽  
Author(s):  
Saeed Behzadipour ◽  
Robert Dekker ◽  
Amir Khajepour ◽  
Edmon Chan
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Manufacturing Industry ◽  
Design Procedure ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Manufacturing Cost ◽  
End Effector ◽  
Serial Manipulators

The growing needs for high speed positioning devices in the automated manufacturing industry have been challenged by robotic science for more than two decades. Parallel manipulators have been widely used for this purpose due to their advantage of lower moving inertia over the conventional serial manipulators. Cable actuated parallel robots were introduced in 1980’s to reduce the moving inertia even further. In this work, a new cable-based parallel robot is introduced. For this robot, the cables are used not only to actuate the end-effector but also to apply the necessary kinematic constraints to provide three pure translational degrees of freedom. In order to maintain tension in the cables, a passive air cylinder is used to push the end-effector against the stationary platform. In addition to low moving inertia, the new design benefits from simplicity and low manufacturing cost by eliminating joints from the robot’s mechanism. The design procedure and the results of experiments will be discussed in the following.

Feasible Motion Solutions for Serial Manipulators at Singular Configurations

2003 ◽  
Vol 125 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Yuefa Fang ◽  
Lung-Wen Tsai
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Full Rank ◽  
Joint Space ◽  
Serial Manipulators ◽  
First Order ◽  
Singular Configurations ◽  
Cartesian Space ◽  
Novel Approach ◽  
Singular Configuration

When a serial manipulator is at a singular configuration, the Jacobian matrix will lose its full rank causing the manipulator to lose one or more degrees of freedom. This paper presents a novel approach to model the manipulator kinematics and solve for feasible motions of a manipulator at singular configurations such that the precise path tracking of a manipulator at such configurations is possible. The joint screw linear dependency is determined by using known line varieties so that not only the singular configurations of a manipulator can be identified but also the dependent joint screws can be determined. Feasible motions in Cartesian space are identified by using the theory of reciprocal screws and the resulting equations of constraint. The manipulator first-order kinematics is then modeled by isolating the linearly dependent columns and rows of the Jacobian matrix such that the mapping between the feasible motions in Cartesian space and the joint space motions can be uniquely determined. Finally, a numerical example is used to demonstrate the feasibility of the approach. The simulation results show that a PUMA-type robot can successfully track a path that is singular at all times.

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