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.

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.

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.

Evaluation of Topological Properties of Parallel Manipulators Based on the Topological Characteristic Indexes

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1381-1399 ◽  
Author(s):  
Huiping Shen ◽  
Ting-Li Yang ◽  
Ju Li ◽  
Dan Zhang ◽  
Jiaming Deng ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Design Guidelines ◽  
Design Knowledge ◽  
Topological Properties ◽  
Topological Characteristic ◽  
Actuated Joints ◽  
Selection Of

SUMMARYThe topological structure of a parallel manipulator (PM) determines its intrinsic topological properties (TPs). The TPs further determine essential kinematic and dynamic properties of the mechanism. TPs can be expressed through topological characteristics indexes (TCI). Therefore, defining a set of TCIs is an important issue to evaluate the TPs of PMs. This article addresses the evaluation of topological properties (ETP) of PMs based on TCI. A general and effective ETP method for PMs is proposed. Firstly, 12 TCIs are proposed, including 8 quantitative TCIs, that is, position and orientation characteristics sets (POC), dimension of the POC set, degrees of freedom (DOF), number of independent displacement equations, types and number of an Assur kinematic chain (AKC), coupling degrees of the AKCs, degrees of redundancy and the number of overs; as well as 4 qualitative TCIs, that is, selection of actuated joints, identification of inactive joints, DOF type and Input–Output motion decoupling. Secondly, the ETP method is illustrated by evaluating some well-known PMs including the Delta, Tricept, Exechon, Z3, H4 and the Gough–Stewart platform manipulators, as well as 28 other typical PMs. Via the ETP analysis of these mechanisms also some valuable design knowledge is derived and guidelines for the design of PMs are established. Finally, a 5-DOF decoupled hybrid spraying robot is developed by applying the design knowledge and the design guidelines derived from the ETP analysis.

scholarly journals The Normal Modes of Nonlinear n-Degree-of-Freedom Systems

1962 ◽  
Vol 29 (1) ◽  
pp. 7-14 ◽  
Author(s):  
R. M. Rosenberg
Keyword(s):  
Linear System ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Minimum Problem ◽  
Infinite Class ◽  
Coupled Equations ◽  
Geometrical Problem ◽  
Maximum Minimum

A system of n masses, equal or not, interconnected by nonlinear “symmetric” springs, and having n degrees of freedom is examined. The concept of normal modes is rigorously defined and the problem of finding them is reduced to a geometrical maximum-minimum problem in an n-space of known metric. The solution of the geometrical problem reduces the coupled equations of motion to n uncoupled equations whose natural frequencies can always be found by a single quadrature. An infinite class of systems, of which the linear system is a member, has been isolated for which the frequency amplitude can be found in closed form.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Planar Motion of a Flexible Beam With a Tip Mass Driven by Two Kinematic Rotational Degrees of Freedom

1998 ◽  
Vol 120 (1) ◽  
pp. 206-213
Author(s):  
D. C. Winfield ◽  
B. C. Soriano
Keyword(s):  
Finite Element Method ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Planar Motion ◽  
Flexible Beam ◽  
The Finite Element Method ◽  
Rotational Degrees Of Freedom ◽  
Tip Mass

The objective was to model planar motion of a flexible beam with a tip mass that is driven by two kinematic rotational degrees of freedom which are (1) at the center of the hub and (2) at the point the beam is attached to the hub. The equations of motion were derived using Lagrange’s equations and were solved using the finite element method. The results for the natural frequencies of the beam especially at high tip masses and high rotational velocities of the hub were calculated and compared to results obtained using the Raleigh-Ritz method. The dynamic response of the beam due to a specified hub rotation was calculated for two cases.

Prediction of On-Stride Walking for Pregnant Women

2010 ◽  
Author(s):  
Jingzhou James Yang ◽  
Qiuling Zou
Keyword(s):  
Pregnant Women ◽  
Human Body ◽  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Weight Changes ◽  
Women's Bodies ◽  
The One ◽  
The Cost ◽  
Recursive Dynamics

Pregnant women’s size, shape, and weight changes have significant effects on their walking stability. Traditionally, experiments are used to study the effects of subjects, but it is time consuming and expensive. This paper presents an optimization-based pregnant women walking simulation with one-stride formulation. The pregnant woman’s model with 55 degrees of freedom (DOFs) is used, including 6 global DOF’s and 49 human body DOF’s. The dynamic equations of motion are based on the recursive dynamics. Without the constraint of symmetry of the human body between two steps within one walking cycle, the study is based on bio-mechanical, human kinematic, and dynamic properties to perform the one-stride simulation, which represent the holonomic and non-holonomic constraints in walking simulation. This forms a nonlinear optimization problem. The summation of all joint actuator torques squared within one stride is the cost function. Nine determinant DOF’s are used to analyze the kinematics and three for dynamics. Three cases (non-pregnancy, 6 month, and 9 month pregnancy) are adopted for the test and investigation. The simulation results show that during the course of pregnancy, pregnant women’s bodies dynamic and kinematic properties change and thus affect their walking and stability.

On Singularities of Planar Parallel Manipulators

1993 ◽  
Author(s):  
H. R. Mohammadi Daniali ◽  
P. J. Zsombor-Murray ◽  
Jorge Angeles
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Classification Scheme ◽  
Parallel Manipulators ◽  
The Other ◽  
Jacobian Matrices ◽  
General Classification ◽  
Three Degrees Of Freedom ◽  
Planar Parallel Manipulators

Abstract The singularities of the Jacobian matrices of two manipulator with three degrees of freedom are analyzed. One is a planar 3-legged manipulator; the other, a planar double-triangular manipulator. A general classification of parallel-manipulator singularities into three groups is described. The classification scheme relies on the properties of the Jacobian matrices of the manipulator. Finally, the three types of singularity are identified for the two manipulators.

Design and Development of H∞ and μ-Synthesis Controllers for Nanorobotic Manipulation and Grasping Applications

2007 ◽  
Author(s):  
Reza Saeidpourazar ◽  
Beshah Ayalew ◽  
Nader Jalili
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Robust Controller ◽  
Accuracy And Precision ◽  
Highly Nonlinear ◽  
Linearized Model ◽  
High Level ◽  
Robust Controller Design

This paper presents the development of H∞ and μ-synthesis robust controllers for nanorobotic manipulation and grasping applications. Here a 3 DOF (Degrees Of Freedom) nanomanipulator with RRP (Revolute Revolute Prismatic) actuator arrangement is considered for nanomanipulation purposes. Due to the sophisticated complexity, and expected high level of accuracy and precision (of the order of 10−7 rad in revolute actuators and 0.25 nm in the prismatic actuator) of the nanomanipulator, there is a need to design a suitable controller to guarantee an accurate manipulation process. However, structure of the nanomanipulator employed here, namely MM3A, is such that the dynamic equations of motion of the nanomanipulator are highly nonlinear and complicated. Linearizing these dynamic equations of the nanomanipulator simplifies the controller design process significantly. However, linearization could suppress some critical information about the system dynamics. In order to achieve the precise motion of the nanomanipulator utilizing the simple linearized model, H∞ and μ-synthesis robust controller design approaches are proposed. Following the development of the controllers, numerical simulations of the proposed controllers on the nanomanipulator are used to verify the positioning performance.

scholarly journals Modular Multibody Formulation for Simulating Off-Road Tracked Vehicles

2014 ◽  
Vol 1 (2) ◽  
pp. 77 ◽  
Author(s):  
Mohamed A Omar
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Dynamic Equations ◽  
Solution Stability ◽  
Simulation Code ◽  
Tracked Vehicles ◽  
Main System ◽  
6 Degrees Of Freedom

This paper presents a formulation and procedure for incorporating the multibody dynamics analysis capability of tracked vehicles in large-scale multibody system.  The proposed self-contained modular approach could be interfaced to any exiting multibody simulation code without need to alter the existing solver architecture.  Each track is modeled as a super-component that can be treated separate from the main system.  The super-component can be efficiently used in parallel processing environment to reduce the simulation time.  In the super-component, each track-link is modeled as separate body with full 6 degrees of freedom (DoF).  To improve the solution stability and efficiency, the joints between track links are modeled as complaint connection.  The spatial algebra operator is used to express the motion quantities and develop the link’s nonlinear kinematic and dynamic equations of motion.  The super-component interacts with the main system through contact forces between the track links and the driving sprocket, the support rollers and the idlers using self-contained force modules.  Also, the super-component models the interaction with the terrain through force module that is flexible to include different track-soil models, different terrain geometries, and different soil properties.  The interaction forces are expressed in the Cartesian system, applied to the link’s equation of motion and the corresponding bodies in the main system.  For sake of completeness, this paper presents dynamic equations of motion of the links as well as the main system formulated using joint coordinates approach.

Sign in / Sign up

Export Citation Format

Share Document