Kinematics of a Pure Translational UPS/3RPaPaR Parallel Mechanism

2007 ◽  
Author(s):  
Chung-Ching Lee ◽  
Po-Chih Lee
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Translational Motion ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Numerical Illustration ◽  
The Matrix ◽  
Kinematic Analyses

From the viewpoint of kinematics, a type of 3 degrees of freedom (dofs) UPS/3RPaPaR overconstrained parallel mechanism (Pa means the hinged 4R parallelogram) with pure translational motion is presented for the development of automatic assembly devices or as a regional structure in the hybrid parallel platform. In the beginning, the formation & mobility are elucidated and the 4×4 transformation matrix & the D-H notation with specific geometric constraints verify the pure translational motion. The forward and inverse kinematic analyses are then established in the analytical closed-form through the matrix method. Besides, we take a numerical illustration for the confirmation of correctness of the derived equations. The determination of workspace is also attained by the intersection of volumes swept by each limb. In addition, the Jacobian matrix and its condition number indicated by Euclidean norm as a function of design parameters are further achieved. Finally, the singularity analysis of the configuration based on the direct and inverse kinematic J-matrix during the movement is identified in detail.

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.

Multi-task oriented design of an asymmetric 3T1R type 4-DOF parallel mechanism

2013 ◽  
Vol 227 (10) ◽  
pp. 2236-2255 ◽  
Author(s):  
Byung-Ju Yi ◽  
Sung Mok Kim ◽  
Hyun Koo Kwak ◽  
Wheekuk Kim
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Parallel Structure ◽  
Design Parameters ◽  
Dynamic Simulations ◽  
Kinematic Modelling ◽  
Lower Mobility ◽  
Manufacturing Applications ◽  
Task Oriented

In performing tasks requiring less than 6 degrees-of-freedom (DOF), lower mobility robots having a parallel structure are effective. This work investigates an asymmetric type 4 degrees-of-freedom parallel mechanism having Schönflies motions. This mechanism would be useful for multi-purpose tasks because it incorporates a transmission linkage with appropriate output modules. The mobility analysis, kinematic modelling, and singularity analysis for the mechanism are performed. Optimal design parameters with respect to both the workspace size and kinematic isotropy are identified by employing composite global design index. In addition, to cope with the singularity problem, a new design involving redundant actuation is suggested. And dynamic simulations are conducted to reaffirm its high potential in real manufacturing applications.

Kinematics of a 3-DOF Translational Parallel Mechanism With 3-PRPaR Topology

2004 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jeng-Hong Chou
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Translational Motion ◽  
Analytical Form ◽  
Inverse Kinematic ◽  
Closed Form Solutions ◽  
The Matrix ◽  
Six Dof ◽  
Singular Configuration ◽  
Algebra Method

From the standpoint of kinematics, we present a type of three-dof pure spatial translational parallel mechanism with 3-PRPaR topology as an alternative to design automation devices and a regional structure of a six-dof hybrid parallel platform. First, we describe the structural properties of mechanism and analyze its kinematic mobility. It is verified that a pure translational motion does exist through the coordinate transformation technique and the well-known D-H parametric notations. Then, we proceed with the forward and inverse kinematic analysis and derive their analytical closed-form solutions by the matrix algebra method. For the confirmation of the derived equations, some numerical examples are also taken. Furthermore, with the help of the forward kinematics, we derive the workspace in the analytical form. Finally, taking account of the overall Jacobian matrix provides the condition number and the identification of singular configuration is explored based on direct and inverse kinematics Jacobian matrix.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

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.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization 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. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

scholarly journals Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

Robotica ◽  
2014 ◽  
Vol 33 (4) ◽  
pp. 747-767 ◽  
Author(s):  
Masayuki Shimizu
Keyword(s):  
Analytical Method ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Target Orientation ◽  
End Effector ◽  
Position And Orientation

SUMMARYThis paper proposes an analytical method of solving the inverse kinematic problem for a humanoid manipulator with five degrees-of-freedom (DOF) under the condition that the target orientation of the manipulator's end-effector is not constrained around an axis fixed with respect to the environment. Since the number of the joints is less than six, the inverse kinematic problem cannot be solved for arbitrarily specified position and orientation of the end-effector. To cope with the problem, a generalized unconstrained orientation is introduced in this paper. In addition, this paper conducts the singularity analysis to identify all singular conditions.

scholarly journals A Translational Three-Degrees-of-Freedom Parallel Mechanism With Partial Motion Decoupling and Analytic Direct Kinematics

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Huiping Shen ◽  
Damien Chablat ◽  
Boxiong Zeng ◽  
Ju Li ◽  
Guanglei Wu ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Design Theory ◽  
Degrees Of Freedom ◽  
Analytic Solutions ◽  
Inverse Kinematic ◽  
Kinematic Modeling ◽  
Topological Design ◽  
Prismatic Joints ◽  
Topological Characteristics ◽  
Three Degrees Of Freedom

Abstract According to the topological design theory and the method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, this paper studied a three-degrees-of-freedom (3-DOF) translational PM that has three advantages, i.e., (i) it consists of three fixed actuated prismatic joints, (ii) the PM has analytic solutions to the direct and inverse kinematic problems, and (iii) the PM is of partial motion decoupling property. First, the main topological characteristics, such as the POC, degree-of-freedom, and coupling degree, were calculated for kinematic modeling. Thanks to these properties, the direct and inverse kinematic problems can be readily solved. Further, the conditions of the singular configurations of the PM were analyzed, which corresponds to its partial motion decoupling property.

Influence Coefficients and Singularity Analysis of a Novel 3-UPU Parallel Mechanism

2017 ◽  
Author(s):  
Ziming Chen ◽  
Dongliang Cheng ◽  
Yang Zhang ◽  
Zhiwei Yang ◽  
Jin Zhou
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Model Simulation ◽  
Hessian Matrix ◽  
Symmetry Plane ◽  
Coefficient Matrix ◽  
Singularity Analysis ◽  
Influence Coefficient ◽  
Parasitic Motion ◽  
Moving Platform

A novel 3-UPU parallel mechanism with two rotational and one translational (2R1T) degrees of freedom (DOFs) is analyzed in this paper. The base and moving platform of this mechanism are always symmetric about a middle symmetry plane. The moving platform can rotate continuously about any axis on the middle symmetry plane, so there exists no parasitic motion during the rotation. Using the kinematic influence coefficient theory and the imaginary mechanism method, the first and second order influence coefficient matrix (namely Jacobian matrix and Hessian matrix) of this mechanism are derived. The relations between the velocity and acceleration of the moving platform and the actuated links are obtained. In order to verify the correctness of the theory, two numerical examples are enumerated and varified by the 3D model simulation. The singularities of this mechanism is discussed and the singular configurations of the mechanism, including one kind of limb singularity and two kinds of platform singularities, are obtained.

Workspace Generation for a 2 - DOF Parallel Mechanism Using Neural Networks

2012 ◽  
Vol 162 ◽  
pp. 121-130 ◽  
Author(s):  
Emilia Campean ◽  
Tiberiu Pavel Itul ◽  
Ionela Tanase ◽  
Adrian Pisla
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Two Degrees Of Freedom ◽  
Initial Testing ◽  
Network Application ◽  
Satellite Dish

The main purpose of the paper is to develop a neural network application destined to the workspace generation of a parallel mechanism, as an performant alternative to the workspace representation based on inverse kinematic model. The paper describes both algorithms. The initial testing was made for a parallel mechanism with two degrees of freedom that could be applied for the orientation of different systems like a TV satellite dish antennas, sun trackers, telescopes, cameras, radars etc.

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