A New Method for Dynamic Modeling of Flexible-Link Flexible-Joint Manipulators

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
M. Vakil ◽  
R. Fotouhi ◽  
P. N. Nikiforuk
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Lagrange Multipliers ◽  
New Method ◽  
Flexible Link ◽  
Flexible Joint ◽  
Generalized Coordinates ◽  
Lagrange’S Equations ◽  
Mass Moment ◽  
Lagrange's Equations

In this article, by combining the assumed mode shape method and the Lagrange’s equations, a new and efficient method is introduced to obtain a closed-form finite dimensional dynamic model for planar Flexible-link Flexible-joint Manipulators (FFs). To derive the dynamic model, this new method separates (disassembles) a FF into two subsystems. The first subsystem is the counterpart of the FF but without joints’ flexibilities and rotors’ mass moment of inertias; this subsystem is referred to as a Flexible-link Rigid-joint manipulator (FR). The second subsystem has the joints’ flexibilities and rotors’ mass moment of inertias, which are excluded from the FR; this subsystem is called Flexible-Inertia entities (FI). While the method proposed here employs the Lagrange’s equations, it neither requires the derivation of the lengthy Lagrangian function nor its complex derivative calculations. This new method only requires the Lagrangain function evaluation and its derivative calculations for a Single Flexible link manipulator on a Moving base (SFM). By using the dynamic model of a SFM and the Lagrange multipliers, the dynamic model of the FR is first obtained in terms of the dependent generalized coordinates. This dynamic model is then projected into the tangent space of the constraint manifold by the use of the natural orthogonal complement of the Jacobian constraint matrix. Therefore, the dynamic model of the FR is obtained in terms of the independent generalized coordinates and without the Lagrange multipliers. Finally, the joints’ flexibilities and rotors’ mass moment of inertias, which are included in the FI, are added to the dynamic model of the FR and a closed-form dynamic model for the FF is derived. To verify this new method, the results of simulation examples, which are obtained from the proposed method, are compared with those of a full-nonlinear finite element analysis, where the comparisons indicate sound agreement

A Constrained Lagrange Formulation of Multilink Planar Flexible Manipulator

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
M. Vakil ◽  
R. Fotouhi ◽  
P. N. Nikiforuk ◽  
H. Salmasi
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Dynamic Equations ◽  
Flexible Link ◽  
Element Analysis ◽  
Constraint Matrix ◽  
Generalized Coordinates

In this article, the closed-form dynamic equations of planar flexible link manipulators (FLMs), with revolute joints and constant cross sections, are derived combining Lagrange’s equations and the assumed mode shape method. To overcome the lengthy and complicated derivative calculation of the Lagrangian function of a FLM, these computations are done only once for a single flexible link manipulator with a moving base (SFLMB). Employing the Lagrange multipliers and the dynamic equations of the SFLMB, the equations of motion of the FLM are derived in terms of the dependent generalized coordinates. To obtain the closed-form dynamic equations of the FLM in terms of the independent generalized coordinates, the natural orthogonal complement of the Jacobian constraint matrix, which is associated with the velocity constraints in the linear homogeneous form, is used. To verify the proposed closed-form dynamic model, the simulation results obtained from the model were compared with the results of the full nonlinear finite element analysis. These comparisons showed sound agreement. One of the main advantages of this approach is that the derived dynamic model can be used for the model based end-effector control and the vibration suppression of planar FLMs.

A study of the free vibration of flexible-link flexible-joint manipulators

2011 ◽  
Vol 225 (6) ◽  
pp. 1361-1371 ◽  
Author(s):  
M Vakil ◽  
R Fotouhi ◽  
P N Nikiforuk ◽  
F Heidari
Keyword(s):  
Joint Stiffness ◽  
Sensitivity Study ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Flexible Link ◽  
Flexible Joint ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Payload Mass ◽  
Analytical Expressions

In this article, explicit expressions for the frequency equation, mode shapes, and orthogonality of the mode shapes of a Single Flexible-link Flexible-joint manipulator (SFF) are presented. These explicit expressions are derived in terms of non-dimensional parameters which make them suitable for a sensitivity study; sensitivity study addresses the degree of dependence of the system’s characteristics to each of the parameters. The SFF carries a payload which has both mass and mass moment of inertia. Hence, the closed-form expressions incorporate the effect of payload mass and its mass moment of inertia, that is, the payload mass and its size. To check the accuracy of the derived analytical expressions, the results from these analytical expressions were compared with those obtained from the finite element method. These comparisons showed excellent agreement. By using the closed-form frequency equation presented in this article, a study on the changes in the natural frequencies due to the changes in the joint stiffness is performed. An upper limit for the joint stiffness of a SFF is established such that for the joint stiffness above this limit, the natural frequencies of a SFF are very close to those of its flexible-link rigid-joint counterpart. Therefore, the value of this limit can be used to distinguish a SFF from its flexible-link rigid-joint manipulator counterpart. The findings presented in this article enhance the accuracy and time-efficiency of the dynamic modeling of flexible-link flexible-joint manipulators. These findings also improve the performance of model-based controllers, as the more accurate the dynamic model, the better the performance of the model-based controllers.

The Analysis of Free-Floating Space Manipulator when Tracking Desired Force/Position

2015 ◽  
Vol 742 ◽  
pp. 560-566
Author(s):  
Long Zhang ◽  
Qing Xuan Jia ◽  
Gang Chen ◽  
Han Xu Sun
Keyword(s):  
Dynamic Model ◽  
Impedance Control ◽  
Position Tracking ◽  
Control Law ◽  
Double Loop ◽  
Space Manipulator ◽  
End Effector ◽  
Loop Control ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

For free-floating space manipulator, a double loop control law is applied to the manipulator to achieve the force/position tracking of the end-effector, and the influence to the manipulator system is analyzed in this paper. First, the dynamic model is established based on Lagrange's equations. On this basis, a double loop control law which is based on the idea of impedance control is applied to the manipulator. During the force/position tracking, the influence of each part of free-floating space manipulator is analyzed, especially the base attitude disturbance. Finally, a simulation is given to show the analyze results.

Dynamic Modeling Based on Screw Theory and Lagrange’s Equations of a 3-DOF Cable-Driven Surgical Instrument

2014 ◽  
Vol 541-542 ◽  
pp. 1039-1042
Author(s):  
Li Ping Xu ◽  
Hong Qiang Sang ◽  
Li Min Chang
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Screw Theory ◽  
Joint Space ◽  
Open Loop ◽  
Surgical Instrument ◽  
Servo Motor ◽  
Lagrange’S Equations ◽  
Relationship Model ◽  
Lagrange's Equations

Dynamic model based on screw theory and Lagrange’s equations including dynamic of servo motor rotor of a 3-DOF cable-driven surgical instrument was established in this paper. Overall dynamic of the 3-DOF cable-driven surgical instrument was performed by dynamic model of the open-loop chain surgical instrument after removal of cables and pulley, the mapping relationship model between the joint space and cable space, and rotor dynamic modeling of servo motor, which is the basic of investigating the overall responses and prosperities of surgical instrument.

METHOD FOR ESTIMATING ERRORS IN MEASURING INSTRUMENTS BY THE SPACE CATALOGUE ORBITS

2018 ◽  
pp. 76-84
Author(s):  
K. V. Sorokin ◽  
E. A. Sunarchina
Keyword(s):  
Dynamic Model ◽  
New Method ◽  
Measuring Instruments ◽  
Measuring Instrument ◽  
Software Complex

Improvement of orbits precision is one of the most important tasks of space surveillance catalogue maintenance. The solution of this problem is directly related to an adequate consideration of the errors of the coordinate information from the measuring instruments. The article consideresd a new method for estimating the precision of measuring instruments on the catalog orbits. To carry out such analysis, in PJSC «VIMPEL» special technological program was created. Main results of a study of radar errors with orbits of space surveillance catalogue was presented. Also, the results were compared with data of measuring instrument's calibration software complex. This software complex provides determination of satellite's position with errors less than 10 m. A new dynamic model of measuring instrument errors is proposed.

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