A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems
01 Jun 1988-Journal of Dynamic Systems Measurement and Control-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 110, Iss: 2, pp 175-181
TL;DR: In this paper, a method for deriving dynamic equations for manipulators containing both rigid and flexible links using Hamilton's principle is presented. But the approach is a natural extension of the well-known Lagrangian method for rigid manipulators.
Abstract: This paper presents a procedure for deriving dynamic equations for manipulators containing both rigid and flexible links. The equations are derived using Hamilton's principle, and are nonlinear integro-differential equations. The formulation is based on expressing the kinetic and potential energies of the manipulator system in terms of generalized coordinates. In the case of flexible links, the mass distribution and flexibility are taken into account. The approach is a natural extension of the well-known Lagrangian method for rigid manipulators. Properties of the dynamic matrices, which lead to a less computation, are shown. Boundary-value problems of continuous systems are briefly described. A two-link manipulator with one rigid link and one flexible link is analyzed to illustrate the procedure.
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TL;DR: A survey of the literature related to dynamic analyses of flexible robotic manipulators has been carried out in this article, where both link and joint flexibility are considered in this work and an effort has been made to critically examine the methods used in these analyses, their advantages and shortcomings and possible extension of these methods to be applied to a general class of problems.
791 citations
Cites methods from "A Lagrangian Formulation of the Dyn..."
...Low and Vidyasagar [222] considered a two-link manipulator with only the last link as a flexible member and used the Lagrangian method to study its dynamics....
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TL;DR: An optical sensing system consisting of a laser diode and a position sensitive detector is introduced for the real-time measurement of the dynamic deflection and a Lyapunov-type controller based on the deflection feedback is proposed to damp out the tip oscillations and regulate the endpoint of the flexible robot.
Abstract: The use of flexible links in a robot inevitably causes the elastic deflection and vibration of the endpoint of the robot during high-speed operations. The deflection and vibration will tend to degrade the positioning performance of the robot. In this paper, an optical sensing system consisting of a laser diode and a position sensitive detector is introduced for the real-time measurement of the dynamic deflection. Utilising a non-linear, coupled and measurement-based dynamic system model, a Lyapunov-type controller based on the deflection feedback is then proposed to damp out the tip oscillations and regulate the endpoint of the flexible robot. Experimental tests are conducted for a flexible one-link robot arm with a payload mass at the tip. The results demonstrate the effectiveness of the proposed measuring and control schemes.
76 citations
01 Apr 1990
TL;DR: A finite-dimensional time-domain dynamic model of a two-link, two-joint planar manipulator is used and emphasis is placed on determining the limitations of control algorithms that use only joint variable-feedback information in calculations of control decisions.
Abstract: The performance limitations of manipulators under joint variable-feedback control are studied as a function of the mechanical flexibility inherent in the manipulator structure. A finite-dimensional time-domain dynamic model of a two-link, two-joint planar manipulator is used in the study. Emphasis is placed on determining the limitations of control algorithms that use only joint variable-feedback information in calculations of control decisions, since most motion control systems in practice are of this kind. Both fine and gross motion cases are studied. Results for fine motion agree well with previously reported results in the literature and are also helpful in explaining the performance limitations in fast gross motions. >
66 citations
TL;DR: Overall dynamic behavior of the manipulator, induced from structural flexibility of the linkage, is well illustrated through simulations, and will be used to develop a prototype parallel manipulator.
Abstract: This paper presents a dynamic model of a planar parallel manipulator including structural flexibility of several linkages. The equations of motion are formulated using the Lagrangian equations of the first type and Lagrangian multipliers are introduced to represent the geometry of multiple closed loop chains. Then, an active damping approach using a PZT actuator is described to attenuate structural vibration of the linkages. Overall dynamic behavior of the manipulator, induced from structural flexibility of the linkage, is well illustrated through simulations. This analysis will be used to develop a prototype parallel manipulator.
60 citations
Cites methods from "A Lagrangian Formulation of the Dyn..."
...where: b̄i =bix ī+biy j̄ and ēi =eix ī+eiy j̄ Cross-multiplication of equation (8) by b̄i gives ̇i = 1 l 2 {[ biy bix eix bix +eiy biy] (b̄i āi ) JPi } ̇̄ XP ẇi (l )/l (10) Acceleration of the moving part can be formulated through a similar procedure as follows;...
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01 Apr 2003
TL;DR: For the first time, Prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator and it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant.
Abstract: In this paper, a mathematical model capable of handling a three-dimensional (3D) flexible n-degree of freedom manipulator having both revolute and prismatic joints is considered. This model is used to study the longitudinal, transversal, and torsional vibration characteristics of the robot manipulator and obtain kinematic and dynamic equations of motion. The presence of prismatic joints makes the mathematical derivation complex. In this paper, for the first time, prismatic joints as well as revolute joints have been considered in the structure of a 3D flexible n-degree of freedom manipulator. The kinematic and dynamic equations of motion representing longitudinal, transversal, and torsional vibration characteristics have been solved in parametric form with no discretization. In this investigation, in order to obtain an analytical solution of the vibrational equations, a novel approach is presented using the perturbation method. By solving the equations of motion, it is shown that mode shapes of the link with prismatic joints can be modeled as the equivalent clamped beam at each time instant. As an example, this method is applied to a three degrees of freedom robot with revolute and prismatic joints. The obtained equations are solved using the perturbation method and the results are used to simulate vibrational behavior of the manipulator.
40 citations