Jerk distribution of a 6–3 Gough-Stewart platform

2003 ◽  
Vol 217 (1) ◽  
pp. 77-84 ◽  
Author(s):  
J Gallardo-Alvarado
Keyword(s):  
Lie Algebra ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Stewart Platform ◽  
Symmetric Form ◽  
Generalized Coordinates ◽  
Numerical Example ◽  
Moving Platform ◽  
Klein Form ◽  
Bilinear Symmetric Form

This paper is devoted to forward and inverse jerk analyses, by means of screw theory, of a Gough-Stewart platform with special topology, namely type 6–3. Given a set of generalized coordinates, and their time derivatives, the reduced jerk state or, for brevity, the jerkor of the moving platform, with respect to the fixed platform, is easily obtained by taking advantage of the properties of the Klein form, a bilinear symmetric form of the Lie algebra, e(3). Finally, the joint rate jerks of the parallel manipulator are found, expressing in screw form the jerkor of the moving platform with respect to the fixed platform. A numerical example is provided.

Synthesis of Parallel Manipulator with Single DOF

2013 ◽  
Vol 330 ◽  
pp. 639-643 ◽  
Author(s):  
Chung Huang Yu ◽  
Wen Yeuan Chung
Keyword(s):  
Parallel Manipulator ◽  
Design Concept ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Numerical Example ◽  
Geometrical Constraints ◽  
Moving Platform ◽  
Manipulator Design

This paper proposed a new manipulator design concept which leads to a single DOF system. The system composed of a moving platform and several supporting legs. It can execute the tasks of 3D body guidance or path generation and thus replace expensive manipulators with high DOF in some conditions. There are mainly two steps in designing this manipulator. The first step is type synthesis to determine the number and types of legs. Dimensional synthesis is then executed based on the movement requirements and geometrical constraints. In this study the reduction of the DOF is also analyzed for various legs added between the moving platform and the ground. A numerical example of executing 3D body guidance is given to verify the proposed new concept.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

scholarly journals A Five-Bar Planar Parallel Manipulator with Two End-Effectors

2018 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Ramon Rodriguez-Castro ◽  
Luciano Perez-Gonzalez ◽  
Carlos R. Aguilar-Najera ◽  
Alvaro Sanchez-Rodriguez
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Intermediate Step ◽  
Euclidean Group ◽  
Planar Parallel Manipulator ◽  
Special Software ◽  
End Effectors ◽  
Klein Form

Parallel manipulators with multiple end-effectors bring us interesting advantages over conventional parallel manipulators such as improved manipulability, workspace and avoidance of singularities. In this work the kinematics of a five-bar planar parallel manipulator equipped with two end-effectors is approached by means of the theory of screws. As an intermediate step the displacement analysis of the robot is also investigated. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that regard the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) plays a central role. In order to exemplify the method of kinematic analysis, a case study is included. Furthermore, the numerical results obtained by means of the theory of screws are confirmed with the aid of special software like ADAMS.TM

Dynamics analysis of a novel 5-DoF parallel manipulator with couple-constrained wrench

Robotica ◽  
2018 ◽  
Vol 36 (10) ◽  
pp. 1421-1435 ◽  
Author(s):  
Yi Lu ◽  
Yang Liu ◽  
Lijie Zhang ◽  
Nijia Ye ◽  
Yongli Wang
Keyword(s):  
Analytical Solutions ◽  
Parallel Manipulator ◽  
3D Model ◽  
Analytic Solution ◽  
Three Dimensional ◽  
Displacement Velocity ◽  
Dynamics Analysis ◽  
Numerical Example ◽  
Moving Platform

SUMMARYA three-dimensional (3D) model of a novel 5-DoF type parallel manipulator with a couple-constrained wrench is constructed and its couple-constrained wrench is analyzed. First, the formulas are derived for solving the displacement, velocity, acceleration of the moving platform and moving links, and a workspace is constructed. Second, the formulas are derived for solving the inertial wrenches of the moving links. Third, a dynamics equation is established by considering the inertial wrenches and friction, and the formulas are derived for solving the dynamically active forces and the dynamically couple-constrained wrench. Finally, a numerical example is given to demonstrate the analytic solution of the kinematics and the dynamics, and the analytical solutions are verified by utilizing a simulation mechanism.

A Simple Method to Solve the Instantaneous Kinematics of the 5-RUR Parallel Manipulator

Robotica ◽  
2019 ◽  
Vol 37 (6) ◽  
pp. 1143-1157 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mohammad H. Abedinnasab ◽  
Md. Nazrul Islam
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Input Output ◽  
Linear Combinations ◽  
Kinematic Constraint ◽  
Simple Method ◽  
Numerical Examples ◽  
Displacement Analysis ◽  
Constraint Equations ◽  
Moving Platform

SummaryIn this work a simple method to solve the kinematics of the 5-R$\underbar{P}$UR parallel manipulator is introduced. Dealing with the displacement analysis, the kinematic constraint equations required to address the forward–inverse displacement analysis are established according to linear combinations of two vectors attached to the moving platform. Then, besides the solution of the inverse displacement analysis two strategies are proposed in order to solve the forward position analysis. Finally, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. Numerical examples are provided with the purpose to illustrate the proposed method. Furthermore, the numerical results obtained by means of screw theory are confirmed with the aid of commercially available software.

Kinematic analysis of a novel 2(3-RUS) parallel manipulator

Robotica ◽  
2015 ◽  
Vol 34 (10) ◽  
pp. 2241-2256 ◽  
Author(s):  
Róger E. Sánchez-Alonso ◽  
José-Joel González-Barbosa ◽  
Eduardo Castillo-Castaneda ◽  
Jaime Gallardo-Alvarado
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Kinematic Model ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Analytical Form ◽  
Planar Geometry ◽  
Moving Platform

SUMMARYThis paper introduces a novel 6-DOF parallel manipulator, which is composed of two 3-RUS parallel manipulators that share a common three-dimensional moving platform. Semi-analytical form solutions are easily obtained to solve the forward displacement analysis of the robot using the non-planar geometry of the moving platform, whereas the velocity, acceleration, and singularity analyses are performed using screw theory. A case study is included to show the application of the kinematic model, which is verified with the aid of a commercially available software. Simple kinematic analysis and reduced singular regions are the main benefits of the proposed parallel manipulator.

Instantaneous Kinematic Characteristics of a Special 3-UPU Parallel Manipulator

2005 ◽  
Author(s):  
Shihua Li ◽  
Zhen Huang
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Initial Position ◽  
Special Structure ◽  
Kinematic Characteristics ◽  
Generic Position ◽  
Parallel Platform ◽  
Moving Platform ◽  
Mechanism Theory

The instantaneous kinematics of a special 3-UPU parallel platform manipulator is discussed in this paper. First, the instantaneous motions of the 3-UPU manipulator in four position and a special manipulator are studied by reciprocal screw theory. Then, the principal screws in one of four position are obtained. It is shown that the moving platform has five DOF (degrees of freedom) in the initial position or after a translation along the Z-axis; in the generic position, the mechanism only has three DOF, moreover the three DOF characteristics are difference in different position. The instantaneous kinematic characteristics of alike 3-UPU mechanisms are very different in different position and special structure. The results presented in this paper are important to the use of alike 3-UPU parallel manipulator and contribute to the mechanism theory.

Performance evaluation of a special 6-PUS type parallel manipulator

Robotica ◽  
2021 ◽  
pp. 1-15
Author(s):  
Xiaochu Liu ◽  
Yunfei Cai ◽  
Weitian Liu ◽  
Linlong Zhang ◽  
Chengxin Hu
Keyword(s):  
Performance Evaluation ◽  
Natural Frequency ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Shaking Table ◽  
Axial Stiffness ◽  
Neutral Position ◽  
Dynamics Model ◽  
Force Transmissibility ◽  
Kane Method

Abstract In this paper, a special 6-PUS parallel manipulator (PM) is utilized as a shaking table. Unlike the existing results about 6-PUS PMs, we make the actuator direction collinear with the linkage direction at neutral position. With respect to the application background, a further analysis of the special PM is carried out from the perspective of motion/force transmissibility, natural frequency and acceleration capability. Specially, the complete dynamics model is established based on the Kane method. Then, generalized transmission indices based on the screw theory are utilized to reflect its motion ability, and a model of natural frequency is proposed with the axial stiffness of linkages considered. Finally, the effect of the angle between the actuator direction and the linkage direction α on various performances is analyzed, and other results are included to illustrate its feasibility and usability.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Design and analysis of CICABOT: a novel translational parallel manipulator based on two 5-bar mechanisms

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 449-456 ◽  
Author(s):  
M. F. Ruiz-Torres ◽  
E. Castillo-Castaneda ◽  
J. A. Briones-Leon
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Geometric Analysis ◽  
Vector Equation ◽  
Prismatic Joints ◽  
Hollow Cylinders ◽  
Moving Platform ◽  
Direct Kinematics

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.

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