Free Vibrations of a Flexible Arm Attached to a Compliant Finite Hub

1988 ◽  
Vol 110 (1) ◽  
pp. 118-120 ◽  
Author(s):  
T. P. Mitchell ◽  
J. C. Bruch
Keyword(s):  
Natural Frequencies ◽  
Free Vibrations ◽  
The Other ◽  
Physical Parameters ◽  
Robot Arm ◽  
Flexible Robot ◽  
Concentrated Mass ◽  
End Effector ◽  
Flexible Arm ◽  
Free Beam

A single-joint flexible robot arm consisting of one link and carrying an end effector is modeled by a continuous, uniform, clamped-free beam having a concentrated mass at the free end and being clamped at the other end to a compliant finite hub. The first six natural frequencies are given for various ratios of physical parameters. The modal shapes are also presented along with their orthogonality relationship. The limiting cases of some of the physical parameters are discussed.

Output Tracking for a Nonlinear Flexible Arm

1993 ◽  
Vol 115 (1) ◽  
pp. 78-85 ◽  
Author(s):  
P. Lucibello ◽  
M. D. Di Benedetto
Keyword(s):  
Rigid Motion ◽  
Inverse System ◽  
Inertial Forces ◽  
Robot Arm ◽  
Bounded Solutions ◽  
Flexible Robot ◽  
Controlled System ◽  
End Effector ◽  
Output Tracking ◽  
Flexible Arm

In this paper, an inversion-based control of the end effector of a two-link flexible robot arm is investigated. The challenge in solving this problem consists in the instability of the inverse system. Arbitrary initialization of the inverse system leads to unbounded elastic vibrations, even if along the desired trajectory the inertial forces associated with the rigid motion are bounded. We show that bounded solutions of the inverse system exist and we provide procedures for computing such solutions in the case of periodic velocities of the end effector. In particular, we consider the case of tracking an unbounded trajectory, e.g., an end point ramp. A technique for the stabilization of the trajectories to be tracked is also proposed and some numerical simulations illustrate the performance of the controlled system.

Compensating Control of a Flexible Robot Arm

1990 ◽  
Vol 2 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Masaru Uchiyama ◽  
◽  
Zhao Hui Jiang ◽  
Kyojiro Hakomori
Keyword(s):  
Control System ◽  
Vibration Suppression ◽  
Hierarchical Control ◽  
Elastic Vibration ◽  
Convergence Condition ◽  
Robot Arm ◽  
Flexible Robot ◽  
End Effector ◽  
Flexible Arm ◽  
Arm Motion

Since the characteristics of flexible robot arm motion is far more complex than that of rigid arm motion due to its link elastic deflections, the flexible arm end-effector positioning problem also becomes more complex. The problem is finally resolved into the following three subproblems: (1) how to suppress the link elastic vibration, (2) how to achieve accurate joint positioning, and (3) how to compensate the end-effector positioning errors due to the link deflections. The problem (1) is being solved by many pieces of work. The problem (2) arises also in the case of rigid arms but, since the joint positioning and link vibration suppressing are coupled, it becomes more complex for the case of flexible arms. The problem (3) is important in order for the arms to perform tasks but no effective method has been presented so far to solve it. This paper presents a hierarchical control system which incorporates organically three control functions: joint positioning, link vibration suppression, and end-effector positioning error compensation. The convergence condition for the compensating control is derived theoretically for the condition of static gravitational loads. The effectiveness of the proposed control system is proved by experiments using a two-link flexible arm. The link deflections are measured by a newly devised and developed sensor consisting of a semiconductor laser and a position sensitive detector (PSD).

Free Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

Control of a Flexible Robot Arm: Experimental and Theoretical Results

1987 ◽  
Vol 109 (4) ◽  
pp. 299-309 ◽  
Author(s):  
N. G. Chalhoub ◽  
A. G. Ulsoy
Keyword(s):  
Partial Evaluation ◽  
Digital Simulation ◽  
Robot Arm ◽  
Flexible Robot ◽  
Motion Controller ◽  
Positional Accuracy ◽  
Spherical Coordinate ◽  
End Effector ◽  
Theoretical Results ◽  
Observation Spillover

The operation of high precision robots is severely limited by. their manipulator dynamic deflection, which persists for a period of time after a move is completed. These unwanted vibrations deteriorate the end effector positional accuracy and reduce significantly the robot arm production rate. A “rigid and flexible motion controller” is derived to introduce additional damping into the flexible motion. This is done by using additional sensors to measure the compliant link vibrations and feed them back to the controller. The existing actuators at the robot joints are used (i.e., no additional actuators are introduced). The performance of the controller is tested on a dynamic model, developed in previous work, for a spherical coordinate robot arm whose last link only is considered to be flexible. The simulation results show a significant reduction in the vibratory motion. The important issue of control and observation spillover is examined and found to present no significant practical problems. Partial evaluation of this approach is performed experimentally by testing two controllers, a “rigid body controller” and a “rigid and flexible motion controller,” on a single joint of a spherical coordinate, laboratory robot arm. The experimental results show a significant reduction in the end effector dynamic deflection; thus partially validating the results of the digital simulation studies.

Neural-Network Based Learning Control of Flexible Mechanism With Application to a Single-Link Flexible Arm

1994 ◽  
Vol 116 (4) ◽  
pp. 792-795 ◽  
Author(s):  
Kazuhiko Takahashi ◽  
Ichiro Yamada
Keyword(s):  
Neural Network ◽  
Angular Position ◽  
Target System ◽  
Space Representation ◽  
Robot Arm ◽  
Flexible Robot ◽  
Neural Network Controller ◽  
Flexible Arm ◽  
Single Link ◽  
Flexible Mechanism

This paper shows the effectiveness of a neural-network controller for controlling a flexible mechanism such as a flexible robot arm. An adaptive-type direct neural controller is formulated using state-space representation of the dynamics of the target system. The characteristics of the controller are experimentally investigated by using it to control the tip angular position of a single-link flexible arm.

Dynamic Finite Element Analysis of the Position Control System of a Two-Link Horizontal Flexible Robot

1990 ◽  
Vol 2 (2) ◽  
pp. 83-90
Author(s):  
Hiroyuki Kojima ◽  
Keyword(s):  
Finite Element ◽  
Control System ◽  
Position Control ◽  
Velocity Curve ◽  
Element Formulation ◽  
Robot Arm ◽  
Flexible Robot ◽  
Element Analysis ◽  
Flexible Arm ◽  
Position Control System

In this paper, a finite element formulation method for a horizontal flexible robot arm with two links is first presented. In the analysis, the kinetic energy of the flexible arm is represented in brief compared with previous methods, and the matrix equation of motion in consideration of the nonlinear forces, such as the Coriolis force, is derived by the finite element method and the variational theorem. Then, the state equation of the mechatronics system consisting of the flexible arm and the position control system is obtained. Secondly, numerical simulations in the case of applying path control based on the trapezoidal velocity curve are carried out by use of the Wilson-<I>θ</I> method, and the effects of the bending rigidity and the shape of the trapezoidal velocity curve on the dynamic characteristics of the mechatronics system are demonstrated.

Nonlinear Regulation of End-Effector Motion for a Flexible Robot Arm

1991 ◽  
pp. 229-236 ◽  
Author(s):  
Alessandro De Luca ◽  
Leonardo Lanari ◽  
Giovanni Ulivi
Keyword(s):  
Robot Arm ◽  
Flexible Robot ◽  
End Effector ◽  
Nonlinear Regulation

Free Vibrations of a Rotating Inclined Beam

2006 ◽  
Vol 74 (3) ◽  
pp. 406-414 ◽  
Author(s):  
Sen Yung Lee ◽  
Jer Jia Sheu
Keyword(s):  
Natural Frequencies ◽  
Beam Theory ◽  
Free Vibrations ◽  
Physical Parameters ◽  
Series Solutions ◽  
Vibration System ◽  
Nonlinear Beam ◽  
Consistent Linearization ◽  
Inclined Beam ◽  
Dynamic Subsystem

By utilizing the Hamilton principle and the consistent linearization of the fully nonlinear beam theory, two coupled governing differential equations for a rotating inclined beam are derived. Both the extensional deformation and the Coriolis force effect are considered. It is shown that the vibration system can be considered as the superposition of a static subsystem and a dynamic subsystem. The method of Frobenius is used to establish the exact series solutions of the system. Several frequency relations that provide general qualitative relations between the natural frequencies and the physical parameters are revealed without numerical analysis. Finally, numerical results are given to illustrate the general qualitative relations and the influence of the physical parameters on the natural frequencies of the dynamic system.

Vibrations of a Clamped Circular Plate Carrying Concentrated Mass

1951 ◽  
Vol 18 (4) ◽  
pp. 349-352
Author(s):  
R. E. Roberson
Keyword(s):  
Circular Plate ◽  
Constant Velocity ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
The Other ◽  
Mass Ratio ◽  
Concentrated Mass ◽  
Resonance Curves

Abstract The vibrations of a circular plate clamped at its edge and carrying a concentrated mass at its center are considered. The plate is excited by a motion of the framing, assumed rigid, to which it is clamped. The first four natural frequencies are displayed graphically as functions of mass ratio, and are calculated more precisely for μ = 0, μ = 0.05, and μ = 0.10. The motions of two subsystems with one degree of freedom are compared, one subsystem being driven by the framing and the other by the concentrated mass on the plate. The plate-mounted subsystem has a response in excess of the response of the framing-mounted subsystem if the framing is suddenly put into motion with constant velocity. Except in the neighborhood of their peaks, whose locations depend upon mass ratio, the subsystem resonance curves are depressed in height by increasing the mass ratio.

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