Branch Identification of Planar Two-DOF Seven-Bar Linkages

2009 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Changyu Xue
Keyword(s):  
Degrees Of Freedom ◽  
Robot Navigation ◽  
Parallel Manipulators ◽  
Companion Paper ◽  
Physical Experiment ◽  
Analysis Method ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Multiple Degrees Of Freedom ◽  
Linkage Synthesis

Mobility identification mainly refers to the problems with the motion continuity and smoothness of a potential design or plan. In any linkage synthesis or robot navigation, it is highly desirable that the ability of any of the numerous design candidates to reach the desired positions in a favorable manner can be determined in a single decisive step automatically rather than through a blind trial or even a physical experiment. Mobility of complex linkages has been one of the most troublesome problems in linkage synthesis and programming and the problem is further complicated with multiple degrees-of-freedom. For multiloop parallel manipulators this paper may represent the first mobility analysis method that can not only decisively and unambiguously rectify motion continuity between discrete positions but also provide clear geometric insight or interpretation regarding the formation of discontinuity. The treatment is based on the principle that the mobility of a multiloop linkage is affected by the mobility of each individual loop as well as the interaction between loops. Since the N-bar rotatability laws govern the mobility of an individual loop, the main mobility issue for multiloop linkages is how the mobility of these loops affects each other. One may find that the concept of joint rotation space (JRS) offers simple and intuitive explanation on how the mobility is affected by the combination of loops. The treatment is very suitable for an automated computer-aided mobility analysis. Examples are employed to demonstrate the proposed method. Continuity is a pivotal issue in linkage mobility analysis. Once the continuity can be rectified, problems with smoothness or singularity, which are discussed in the companion paper [28], can be resolved.

Enumeration and instantaneous mobility analysis of a class of 3-UPU parallel manipulators with equilateral triangular platforms

Robotica ◽  
2021 ◽  
pp. 1-32
Author(s):  
Sercan Boztaş ◽  
Gökhan Kiper
Keyword(s):  
Software Package ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Mobility Analysis ◽  
Specific Design ◽  
Design Task ◽  
Moving Platforms ◽  
Joint Axis ◽  
Motion Characteristics

Abstract In this study, several joint axis orientations on equilateral platforms and the limbs of 3-UPU parallel manipulators (PMs) are examined. The generated joint layouts for the platforms were matched with each other to generate and enumerate manipulator architectures based on certain assumptions. The structures of thus obtained manipulators are examined and limb types were determined. These limb types were analyzed using screw theory. The instantaneous mobility of the manipulators and the motion characteristics of the moving platforms are tabulated. The finite mobility analysis of one of the manipulators is performed using a software package as an example. Among several different 3-UPU PM architectures, 118 novel 3-UPU PMs with non-parasitic 3-degrees-of-freedom are significantly important. The classified 3-UPU PMs with determined motion characteristics can be used by researchers as a design alternative for their specific design task.

Mobility Analysis of Parallel Manipulators and Pattern of Transform Matrix

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Chao Chen
Keyword(s):  
Degrees Of Freedom ◽  
Pattern Analysis ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Fundamental Issue ◽  
Mobility Analysis ◽  
Geometric Conditions ◽  
Special Cases ◽  
Transform Matrix ◽  
And Robotics

The mobility or degrees of freedom is a fundamental issue in mechanisms and robotics. In this work, we investigate the mobility of parallel manipulators from a new point of view, and introduce a new concept, the pattern of transform matrix. It is shown that both general and modified Chebychev–Gruble–Kutzbach formulas are the special cases of the pattern analysis. We further propose a framework upon the pattern analysis of transform matrix to calculate the mobility, to evaluate the property of the motion, and to determine the exact-actuation arrangement. The proposed approach should be general enough to evaluate any existing parallel manipulator. Five parallel manipulators with special geometric conditions and lower mobilities are discussed.

Locally Linearized Dynamic Analysis of Parallel Manipulators and Application of Input Shaping to Reduce Vibrations

2004 ◽  
Vol 126 (1) ◽  
pp. 156-168 ◽  
Author(s):  
Kris Kozak ◽  
Imme Ebert-Uphoff ◽  
William Singhose
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Model Simulation ◽  
Parallel Architecture ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Dynamic Equations ◽  
Input Shaping ◽  
Multiple Degrees Of Freedom

Input Shaping is a technique that seeks to reduce residual vibrations through modification of the reference command given to a system. Namely the reference command is convolved with a suitable train of impulses. Input shaping has proven to be successful in reducing the vibrations of a great variety of linear systems. This article seeks to apply input shaping to robotic manipulators of parallel architecture. Such systems have multiple degrees-of-freedom and non-linear dynamics and therefore standard input shaping techniques cannot be readily applied. In order to apply standard input shaping techniques to such systems, this article linearizes the dynamic equations of the system locally and determines the configuration-dependent natural frequencies and damping ratios throughout its workspace. Techniques are developed to derive the dynamic equations directly in linearized form. The method is demonstrated for a sample manipulator with two degrees-of-freedom. A linearized dynamic model is derived and input shaping is locally tuned according to the linearized dynamic model. Simulation results are provided and discussed.

Singularity and Sub-Branch Identification of Two-DOF Seven-Bar Parallel Manipulators

2009 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Changyu Xue ◽  
Kenneth R. Currie
Keyword(s):  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Simple Explanation ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Computer Aided ◽  
Center Position ◽  
Planar Linkages ◽  
General Method ◽  
Unified Method

Mobility analysis of multi-DOF multiloop planar linkages is much more complicated than the single-DOF planar linkages and has been little explored. This paper offers a unified method to treat the singularity (dead center position) and sub-branch identification of the planar two-DOF seven-bar linkages regardless of the choice of the inputs or fixed links. This method can be extended for the singularity analysis of other multi-DOF multiloop linkages. Based on the concept of joint rotation space and N-bar rotatability laws, this paper presents a general method for the sub-branch identification of the seven-bar linkages. It offers simple explanation and geometric insights for the formation of branch, singularity and sub-branch of the two-DOF seven-bar linkages. The presented algorithm for sub-branch identification is suitable for automated computer-aided mobility identification. Examples are employed to demonstrate the proposed method.

A Method to Evaluate and Calculate the Mobility of a General Compliant Parallel Manipulator

2004 ◽  
Author(s):  
Jingjun Yu ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Parallel Manipulators ◽  
Kinematic Characteristic ◽  
Parallel Kinematic Machine ◽  
Compliance Matrix ◽  
Multiple Degrees Of Freedom ◽  
Parallel Kinematic

A compliant parallel manipulator (CPM), is a kind of compliant mechanism characterizes a complicate topological structure and multiple degrees of freedom. As one of the kinematic characteristics of a CPM, the mobility of a CPM become complicate compared to its rigid-counterpart. In order to describe such a complicate kinematic characteristic of a CPM, “primary mobility of a compliant parallel manipulator” concept is proposed. By means of the screw theory, a method of quantifying the primary mobility of the CPM is investigated under the ground that the compliance matrix of the manipulator should be calculated primarily. By using this method, the primary mobility of two typical compliant parallel manipulators, one is a planar 3-RRR CPM and the other a spatial 3-RRPR CPM, is addressed respectively. This proposed method is also instructive for analyzing the instantaneous mobility of a general degenerate-DOF parallel manipulator or a Parallel Kinematic Machine (PKM).

Joint Rotation Space, Workspace, and Singularity-Free Workspace of Parallel Five-Bar Manipulators

2000 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Yi Zhang
Keyword(s):  
Trajectory Planning ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Extensive Study ◽  
Open Loop ◽  
Joint Rotation ◽  
One To One ◽  
The One

Abstract Closed-loop manipulators, while offering some advantages over the open-loop manipulators, also introduce new topics of study such as their joint rotation space (JRS) and workspace. In the previous studies, the concept of JRS was very effective in the study of the allowable inputs of five-bar linkages[11], and the concepts of sheet and side[7] were later introduced for the purpose of clearly describing all of the joint rotation spaces associated to a parallel manipulator with two degrees of freedom. However, of the two types of singularity of parallel manipulators, only the uncertainty singularity was considered in the aforementioned studies. The stationarity singularity was not indicated in the JRS of the manipulators, which would not be sufficient in the design and trajectory planning of parallel manipulators where the one-to-one correspondence between the JRS and the wrist point workspace would be required. This paper reports an extensive study on the JRS and singularity-free workspace of the parallel five-bar manipulators. The objective of the study is to establish a one-to-one corresponding relationship between the JRS and singularity-free workspace. A concise and sufficient way is proposed to thoroughly recognize the JRS and workspace of the parallel five-bar manipulators. The result can be applied in the design and trajectory planning of parallel five-bar manipulators, and the concepts can be extended to other parallel manipulators.

scholarly journals Screw-System-Based Mobility Analysis of a Family of Fully Translational Parallel Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ernesto Rodriguez-Leal ◽  
Jian S. Dai ◽  
Gordon R. Pennock
Keyword(s):  
System Approach ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
System Analysis ◽  
Parallel Manipulators ◽  
Mobility Analysis ◽  
Redundant Constraints ◽  
The Common

This paper investigates the mobility of a family of fully translational parallel manipulators based on screw system analysis by identifying the common constraint and redundant constraints, providing a case study of this approach. The paper presents the branch motion-screws for the 3-RP̲C-Y parallel manipulator, the 3-RCC-Y (or 3-RP̲RC-Y) parallel manipulator, and a newly proposed 3-RP̲C-T parallel manipulator. Then the paper determines the sets of platform constraint-screws for each of these three manipulators. The constraints exerted on the platforms of the 3-RP̲Carchitectures and the 3-RCC-Y manipulators are analyzed using the screw system approach and have been identified as couples. A similarity has been identified with the axes of couples: they are perpendicular to theRjoint axes, but in the former the axes are coplanar with the base and in the latter the axes are perpendicular to the limb. The remaining couples act about the axis that is normal to the base. The motion-screw system and constraint-screw system analysis leads to the insightful understanding of the mobility of the platform that is then obtained by determining the reciprocal screws to the platform constraint screw sets, resulting in three independent instantaneous translational degrees-of-freedom. To validate the mobility analysis of the three parallel manipulators, the paper includes motion simulations which use a commercially available kinematics software.

Experimental Validation of Jacobian-Based Stiffness Analysis Method for Parallel Manipulators With Nonredundant Legs

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Antonius G. L. Hoevenaars ◽  
Clément Gosselin ◽  
Patrice Lambert ◽  
Just L. Herder
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Experimental Validation ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Stiffness Analysis ◽  
Levels Of Detail ◽  
Structural Compliance

A complete stiffness analysis of a parallel manipulator considers the structural compliance of all elements, both in designed degrees-of-freedom (DoFs) and constrained DoFs, and also includes the effect of preloading. This paper presents the experimental validation of a Jacobian-based stiffness analysis method for parallel manipulators with nonredundant legs, which considers all those aspects, and which can be applied to limited-DoF parallel manipulators. The experimental validation was performed by comparing differential wrench measurements with predictions based on stiffness analyses with increasing levels of detail. For this purpose, two passive parallel mechanisms were designed, namely, a planar 3DoF mechanism and a spatial 1DoF mechanism. For these mechanisms, it was shown that a stiffness analysis becomes more accurate if preloading and structural compliance are considered.

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

scholarly journals Design, Fabrication, and Testing of a Novel 3D 3-Fingered Electrothermal Microgripper with Multiple Degrees of Freedom

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 444
Author(s):  
Guoning Si ◽  
Liangying Sun ◽  
Zhuo Zhang ◽  
Xuping Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Polyimide Film ◽  
Zebrafish Embryos ◽  
Multiple Degrees Of Freedom ◽  
Electrothermal Actuator ◽  
3D Space ◽  
Pick And Place

This paper presents the design, fabrication, and testing of a novel three-dimensional (3D) three-fingered electrothermal microgripper with multiple degrees of freedom (multi DOFs). Each finger of the microgripper is composed of a V-shaped electrothermal actuator providing one DOF, and a 3D U-shaped electrothermal actuator offering two DOFs in the plane perpendicular to the movement of the V-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with the polyimide film. The durability of the polyimide film is tested under different voltages. The static and dynamic properties of the finger are also tested. Experiments show that not only can the microgripper pick and place microobjects, such as micro balls and even highly deformable zebrafish embryos, but can also rotate them in 3D space.

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