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.

Analysis of Varying Natural Frequencies and Damping Ratios of a Sample Parallel Manipulator Throughout its Workspace Using Linearized Equations of Motion

2001 ◽  
Author(s):  
Kris Kozak ◽  
Imme Ebert-Uphoff ◽  
William Singhose
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Parallel Architecture ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Dynamic Equations ◽  
Extreme Variation

Abstract This article investigates the dynamic properties of robotic manipulators of parallel architecture. In particular, the dependency of the dynamic equations on the manipulator’s configuration within the workspace is analyzed. The proposed approach is to linearize the dynamic equations locally throughout the workspace and to plot the corresponding natural frequencies and damping ratios. While the results are only applicable for small velocities of the manipulator, they present a first step towards the classification of the nonlinear dynamics of parallel manipulators. The method is applied to a sample manipulator with two degrees-of-freedom. The corresponding numerical results demonstrate the extreme variation of its natural frequencies and damping ratios throughout the workspace.

Oscillation Reduction and Frequency Analysis of Under-Constrained Cable-Driven Parallel Robot with Three Cables

Robotica ◽  
2019 ◽  
Vol 38 (3) ◽  
pp. 375-395 ◽  
Author(s):  
Sung Wook Hwang ◽  
Jeong-Hyeon Bak ◽  
Jonghyun Yoon ◽  
Jong Hyeon Park
Keyword(s):  
Frequency Analysis ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Vibration Suppression ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Input Shaping ◽  
End Effector ◽  
Multi Mode

SummaryCable-driven parallel robots (CDPRs) possess a lot of advantages over conventional parallel manipulators and link-based robot manipulators in terms of acceleration due to their low inertia. This paper deals with under-constrained CDPRs, which manipulate the end-effector to carrying the payload by using a number of cables less than six, often used preferably owing to their simple structures. Since a smaller number of cables than six are used, the end-effector of CDPR has uncontrollable degrees of freedom and that causes swaying motion and oscillations. In this paper, a scheme to curb on the unwanted oscillation of the end-effector of the CDPR with three cables is proposed based on multimode input shaping. The precise dynamic model of the under-constrained CDPR is obtained to find natural frequencies, which depends on the position of the end-effector. The advantage of the proposed method is that it is practicable to generate the trajectories for vibration suppression based on multi-mode input-shaping scheme in spite of the complexity in the dynamics and the difficulty in computing the natural frequencies of the CDPR, which are required in any input-shaping scheme. To prove the effectiveness of the proposed method, computer simulations and experiments were carried out by using 3-D motion for CDPR with three cables.

A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Jun Wu ◽  
Binbin Zhang ◽  
Liping Wang
Keyword(s):  
Dynamic Model ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Maximum Acceleration ◽  
Virtual Work Principle ◽  
Joint Force ◽  
Joint Forces ◽  
Three Degrees Of Freedom

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

A new high dimension nonlinear dynamics simulation model for four-wheel-steering vehicle

2012 ◽  
Vol 227 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Wei Wang ◽  
Yuling Song
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Friction Model ◽  
Dynamics Simulation ◽  
Dynamic Prediction ◽  
Turning Angle ◽  
Multiple Degrees Of Freedom ◽  
Nonlinear Dynamic Characteristic ◽  
Novel Method ◽  
Tire Friction

A novel method and process that produce the multiple-degrees-of-freedom dynamic model of four-wheel-steering vehicle is proposed for dynamic prediction. It can avoid disadvantages of half-baked expression by simple linear dynamic model through thinking about nonlinear specialty of tire and applying two-dimensional LuGre tire friction model. The complexity caused by the unit of suspension which has absolute value elasticity and subsection linear damper is solved during modeling. Based on control law of turning angle, nonlinear dynamic characteristic of four-wheel-steering vehicle is calculated under the condition of small disturbance. The experiment supports the model and confirms a series of simulation results by Matlab 7.0.

Static and Vibration Analyses of a Three-Dimensional Snake-Like Micropositioning Stage

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Nicola Scuor ◽  
Paolo Gallina ◽  
Marco Giovagnoni
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Dynamic Tests ◽  
Lumped Mass ◽  
Simulation Data ◽  
End Effector ◽  
Three Degrees Of Freedom

This paper presets three degrees of freedom (DOF) piezoelectric micropositioning stage. The stage is composed of a stack of piezodisk bender actuators actuated in such a way to prevent the end-effector from rotating; this way the end-effector can only translate along the x, y, and z axes. Thanks to its snake-like configuration, the system is capable of large displacements (of the order of 50 μm) with low driving voltages (of the order of 100 V). Several lumped-mass static and dynamic models of the device have been implemented. Static experimental results, which are in agreement with simulation data, confirmed the performances of the device. A dynamic model showed the natural frequencies of the mechanism. Also dynamic tests have been conducted in order to validate the dynamic model.

Passively Adaptive Compliant Gripper

2012 ◽  
Vol 162 ◽  
pp. 316-325 ◽  
Author(s):  
Dalibor Petkovic ◽  
Mirna Issa ◽  
Nenad D. Pavlovic ◽  
Lena Zentner
Keyword(s):  
Silicone Rubber ◽  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Robotic Manipulators ◽  
Embedded Sensors ◽  
Control Algorithms ◽  
Underactuated Mechanism ◽  
Complex Control ◽  
Multiple Degrees Of Freedom ◽  
Conductive Silicone Rubber

Gripping and holding of objects are key tasks for robotic manipulators. The development of universal grippers able to pick up unfamiliar objects of widely varying shapes and surfaces is a very challenging task. Passively compliant underactuated mechanisms are one way to obtain the gripper which could accommodate to any irregular and sensitive grasping objects. The purpose of the underactuation is to use the power of one actuator to drive the open and close motion of the gripper. The underactuation can morph shapes of the gripper to accommodate to different objects. As a result, they require less complex control algorithms. The fully compliant mechanism has multiple degrees of freedom and can be considered as an underactuated mechanism. This paper presents a new design of the adaptive underactuated compliant gripper with distributed compliance and embedded sensors in the gripper structure. The adaptive gripper surfaces will have the sensing capability by these embedded sensors. The gripper will be made of a silicone rubber and conductive silicone rubber will be used for the embedded sensors. The main points of this paper are in explanation of the construction and production of the gripper structure and showing the methodology of a new sensing capability of the gripper.

scholarly journals Rigid-Flexible Modal Analysis of the Hydraulic 6-DOF Parallel Mechanism

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1604
Author(s):  
Chenyang Zhang ◽  
Hongzhou Jiang
Keyword(s):  
Dynamic Model ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Hydraulic Cylinder ◽  
Flexible Structure ◽  
Actual Performance ◽  
Experimental Platform ◽  
Response Characteristics ◽  
Dynamic Response Characteristics

In view of the problems encountered in previous hydraulic 6-DOF parallel mechanism projects, flexible modes appear that the actual natural frequencies of x and y degrees of freedom of the parallel mechanism are lower than those obtained through calculation. The phenomenon above not only decreases the dynamic response characteristics of the mechanism, but also leads to doubts about the actual performance of the mechanism. The real reason for the phenomenon above is solved in this paper. First the flexible structure of the hydraulic cylinder is analyzed and simplified, and then the dynamic model of the rigid-flexible 6-DOF parallel mechanism is established with the extended Hamilton’s principle. Finally the rigid-flexible modes are calculated with the dynamic model obtained, further analysis and verification with a simulation model and an experimental platform are also conducted. Results show that the phenomenon of the flexible modes is mainly caused by the O-rings of the step-seals of the guide sleeve and those with less elasticity should be adopted to keep the dynamic characteristics of the parallel mechanism.

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.

Automated Symbolic Derivation of Dynamic Equations of Motion for Robotic Manipulators

1986 ◽  
Vol 108 (3) ◽  
pp. 172-179 ◽  
Author(s):  
M. C. Leu ◽  
N. Hemati
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Dynamic Equations ◽  
Computer Memory ◽  
Symbolic Language ◽  
Symbolic Form ◽  
General Computer Program ◽  
Lagrange Formalism ◽  
General Computer

A general computer program for deriving the dynamic equations of motion for robotic manipulators using the symbolic language MACSYMA has been developed. The program, developed based on the Lagrange formalism, is applicable to manipulators of any number of degrees of freedom. Examples are given to illustrate how to use this program for dynamic equation generation. Advantages of expanding the dynamic equations into symbolic form are presented. Techniques for improving efficiency of equation generation, overcoming computer memory limitation, and approximating manipulator dynamics are discussed.

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