Robot Manipulator Trajectory Synthesis for Minimal Vibrational Excitation

1997 ◽  
Author(s):  
W. Kim ◽  
J. Rastegar
Keyword(s):  
Robot Manipulator ◽  
Vibrational Excitation ◽  
High Harmonic ◽  
Harmonic Excitation ◽  
Tracking Accuracy ◽  
Natural Modes ◽  
Starting Point ◽  
Modes Of Vibration ◽  
Operating Space ◽  
Harmonic Components

Abstract As a robot manipulator is forced to track a given trajectory, the required actuating torques (forces) may excite the natural modes of vibration of the system. Due to their nonlinear dynamics, internally and externally induced high harmonic excitation torques are generally generated even though such harmonics have been eliminated from the synthesized trajectories and filtered from the drive inputs. It is therefore desirable to synthesize trajectories such that the actuating torques required to realize them do not contain higher harmonic components with significant amplitudes. In this paper, a systematic method is presented for synthesizing such trajectories. With such trajectories, a robot manipulator can operate at higher speeds and achieve higher tracking accuracy with suppressed residual vibration. It is shown that in general and for a given starting point, such trajectories can only be synthesized to a portion of the operating space of the manipulator. The method is developed based on the Trajectory Pattern Method (TPM). The application of the method to optimal trajectory synthesis for a plane 2R manipulator is presented.

Trajectory Synthesis and Redundancy Resolution for High Speed Point to Point Motions of Redundant Robot Manipulators

1997 ◽  
Author(s):  
W. Kim ◽  
J. Rastegar
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Dynamic Performance ◽  
High Harmonic ◽  
Harmonic Excitation ◽  
Redundancy Resolution ◽  
Tracking Accuracy ◽  
Point To Point

Abstract Trajectory synthesis for robot manipulators with redundant kinematic degrees-of-freedom has been studied by numerous investigators. Redundant manipulators are of interest since the redundant degrees-of-freedom can be used to improve the local and global kinematic and dynamic performance of a system. As a robot manipulator is forced to track a given trajectory, the required actuating torques (forces) may excite the natural modes of vibration of the system. Noting that manipulators with revolute joints have nonlinear dynamics, high harmonic excitation torques are generally generated even though such harmonics have been eliminated from the synthesized trajectories and filtered from the drive inputs. In this paper, a redundancy resolution method is developed based on the Trajectory Pattern Method (TPM) to synthesize trajectories such that the actuating torques required to realize them do not contain higher harmonic components with significant amplitudes. With such trajectories, a robot manipulator can operate at higher speeds and achieve higher tracking accuracy with suppressed residual vibration. As an example, optimal trajectories are synthesized for point to point motions of a plane 3R manipulator.

Linkage Mechanisms With Cam-Integrated Joints for Controlled Harmonic Content of the Output Motion: Theory and Application

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
L. Yuan ◽  
J. Rastegar ◽  
J. Zhang
Keyword(s):  
Closed Loop ◽  
Vibrational Excitation ◽  
High Harmonic ◽  
Harmonic Component ◽  
Linkage Mechanism ◽  
Mechanism Synthesis ◽  
Cam Mechanism ◽  
Harmonic Content ◽  
Harmonic Components ◽  
Four Bar Linkage

In a recent study, the authors presented a systematic method for the modification of the output motion of linkage mechanisms with closed-loop chains using cams positioned at one or more joints of the mechanism. In this paper, the method is applied to the design of a linkage mechanism with an integrated cam mechanism to eliminate high harmonic component of the output motion. The mechanism may be synthesized using any existing linkage mechanism synthesis technique. In the present study, a cam mechanism is synthesized to eliminate all high harmonic components of the output link motion of a four-bar linkage mechanism to illustrate the potentials of the present approach. The mechanism is then constructed and successfully tested. With the present method, selected ranges of high harmonic motions generated due to the mechanisms kinematics nonlinearity can be eliminated by integrating appropriately designed cams, thereby significantly reducing the potential vibrational excitation that the mechanism can impart on the overall system, including its own structure. Such systems should therefore be capable of operating at higher speeds and with increased precision.

scholarly journals ІНТЕРПРЕТАЦІЯ ВІБРАЦІЙНИХ СИГНАЛІВ СКЛАДНОЇ РОТОРНОЇ СИСТЕМИ НА ОСНОВІ ФРАКТАЛЬНОГО АНАЛІЗУ

2019 ◽  
pp. 114-121
Author(s):  
Надія Іванівна Бурау ◽  
Ольга Ярославівна Паздрій
Keyword(s):  
Hurst Exponent ◽  
Additive Noise ◽  
Harmonic Excitation ◽  
Rotor Speed ◽  
Vibration Signals ◽  
Vibration Excitation ◽  
Modes Of Vibration ◽  
Stationary Vibration ◽  
Harmonic Components

The work analyzes vibration signals obtained by simulating a turbine of a complex rotor system, for example, an aviation gas turbine engine, under conditions of stationary and non-stationary excitations. Four modes of vibration excitation are considered: stationary poly-harmonic excitation with the frequency of rotor rotation and super-harmonic components; stationary poly-harmonic excitation with the frequency of rotor rotation and sub-harmonic components; non-stationary vibration excitation with a linear increase in the rotor speed with super-harmonic and sub-harmonic components of the instantaneous rotor speed. In the course of the turbine model, vibration signals are generated, which are further analyzed without taking into account and taking into account additive noise. For signal processing, fractal and time-scale (wavelet) analysis were used. The determination of the fractal structure of the simulated vibration signals is made based on R / S analysis, or the method of normalized scope, as a result of which the Hurst exponent is determined. The Hurst exponent is a number that is interpreted as the ratio of the “strength” of a trend to the signal noise level and is used in the study to interpret the received vibration signals. The results showed that the vibration signals obtained in all considered modes of vibration excitation without taking into account the additive noise, in terms of the Hurst exponent, are classified as anti-persistent trend-non-stable signals. Taking into account additive noise, the Hurst exponent increases, the vibration properties in stationary excitation modes approach persistence and the appearance of a trend, and in non-stationary vibration excitation signals approach to processes such as white noise. For the vibration signal obtained at stationary poly-harmonic excitation with super-harmonic components, a preliminary wavelet - decomposition was carried out into a set of approximations and details, followed by determination of the Hurst exponent for each element of decomposition. The results obtained showed an ambiguous change in the Hurst exponent for various decomposition elements. The obtained results can be used to improve the methodological and algorithmic support systems for functional diagnostics of complex rotor systems with the appearance and propagation of damage to their rotating elements.

scholarly journals A corner smoothing algorithm using Trajectory Pattern Method (TPM) for high-speed and high-quality machining

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110406
Author(s):  
Hao Li ◽  
Jahangir Rastegar ◽  
Baosheng Wang ◽  
Wenjiang Wu ◽  
Zhuwen Yan
Keyword(s):  
Fundamental Frequency ◽  
High Harmonic ◽  
Transition Curve ◽  
Smoothing Algorithm ◽  
Machining Efficiency ◽  
Modes Of Vibration ◽  
Trajectory Pattern ◽  
Harmonic Components ◽  
Feed Drive System ◽  
Trajectory Pattern Method

In micro-line segments machining, transition curves with high harmonic components are more prone to causing vibration issues in the feed drive system, which affects machining efficiency and quality severely. To construct low harmonic trajectories, this paper proposes a corner smoothing algorithm that uses the Trajectory Pattern Method (TPM). The transition curve construction and axial motion scheduling are performed with a specified fundamental frequency in one step, which reduces the smoothing process time and avoids excitation of natural modes of vibration of the system. The synthesized trajectories and axial kinematic profiles are all smooth and only contain the selected fundamental frequency and its first two odd harmonics, which minimizes the number of high harmonic components in the required actuation forces/torques and avoids excitation of the system modes of vibration. Linear programming is used to synthesize the trajectories. The proposed algorithm is shown to achieve near time-optimal trajectories. The provided experimental analysis and comparisons demonstrate that the proposed algorithm achieves smooth axial kinematic profiles with low harmonic contents, which would improve machining efficiency and quality.

Large Amplitude Vibrations of Completely Free Rectangular Plates

2012 ◽  
Author(s):  
F. Alijani ◽  
M. Amabili
Keyword(s):  
Shear Deformation Theory ◽  
Energy Functional ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Geometric Imperfections ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Collocation Scheme ◽  
Large Amplitude Vibrations

Nonlinear forced vibrations of completely free rectangular plates are studied using multi-modal Lagrangian approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. Geometric imperfections are taken into account. The analysis is carried out in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is conducted to obtain the natural frequencies and mode shapes. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained. A pseudo arc-length continuation and collocation scheme is employed to carry out a bifurcation analysis. The effect of number of modes retained in the approximation, thickness ratio and geometric imperfections on the trend of nonlinearity is discussed.

Integration of Smart Actuators in the Structure of Robots for High-Speed and Precision Object Manipulation

2001 ◽  
Author(s):  
Jahangir S. Rastegar ◽  
Lifang Yuan
Keyword(s):  
High Speed ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
High Harmonic ◽  
Object Manipulation ◽  
Smart Actuators ◽  
Computer Controlled ◽  
Harmonic Components ◽  
Joint Motions ◽  
And Control

Abstract A systematic method is presented for optimal integration of smart actuators into the structure of robot manipulators for the purpose of enabling them to perform smooth object manipulation with smooth actuated joint motions. Here, the motions are considered to be smooth if they do not contain high harmonic components. For optimal positioning of smart actuators in the structure of robot manipulators, a method is developed based on the evaluation of the transmissibility of displacement (velocity and/or force) from the smart actuators to the robot manipulator joint motions and the end-effector displacements (velocity and/or force). A method is then presented for synthesizing actuated joint and object motions to achieve trajectories that do not contain high harmonic components. By minimizing the high harmonic components of the required joint and object motions with properly sized and placed smart actuators, such computer-controlled machines can operate at relatively higher speeds and achieve greater tracking precision with minimal vibration and control problems. A number of numerical examples are provided.

Large Amplitude Vibrations of Laminated Rectangular Plates With Free Edges

2013 ◽  
Author(s):  
F. Alijani ◽  
M. Amabili
Keyword(s):  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Energy Functional ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Collocation Scheme ◽  
Large Amplitude Vibrations

Nonlinear forced vibrations of completely free laminated composite rectangular plates are studied using multi-modal Lagrangian approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. The numerical analysis is conducted in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is performed to obtain the natural frequencies and mode shapes. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained. A pseudo arc-length continuation and collocation scheme is employed to carry out a bifurcation analysis. A consistent reduced-order model necessary to capture the nonlinear dynamics of the plate is developed and the effect of number of modes retained in the numerical model is discussed.

Optimal Smart Actuator Integration to Reduce Vibration in High Speed Mechanical Systems

2001 ◽  
Author(s):  
J. Rastegar ◽  
L. Yuan ◽  
L. Hua
Keyword(s):  
High Speed ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
High Harmonic ◽  
Smart Actuators ◽  
Computer Controlled ◽  
Harmonic Components ◽  
Smart Actuator ◽  
Joint Motions ◽  
And Control

Abstract A systematic method is presented for optimal integration of smart actuators into the structure of robot manipulators for the purpose of enabling them to perform smooth object manipulation with smooth actuated joint motions. Here, the motions are considered to be smooth if they do not contain high harmonic components. For optimal positioning of smart actuators in the structure of robot manipulators, a method is developed based on the evaluation of the transmissibility of displacement (velocity and/or force) from the smart actuators to the robot manipulator joint motions and the end-effector displacements (velocity and/or force). A method is then presented for synthesizing actuated joint and object motions to achieve trajectories that do not contain high harmonic components. By minimizing the high harmonic components of the required joint and object motions with properly sized and placed smart actuators, such computer-controlled machines can operate at relatively higher speeds and achieve greater tracking precision with minimal vibration and control problems. A number of numerical examples are provided.

The Effects of the Manipulator Type on the Vibrational Excitation During Motion

1992 ◽  
Author(s):  
Q. Tu ◽  
Jahangir Rastegar
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Vibrational Excitation ◽  
Mechanical Systems ◽  
Average Energy ◽  
Structural Type ◽  
Higher Harmonics ◽  
Modes Of Vibration ◽  
Prismatic Joints ◽  
And Control

Abstract The relationship between the structural type of a manipulator and its susceptibility to motion induced vibrational excitation is examined. For manipulators of different type, the average potential resonant energy transfer to a robot manipulator system by the higher harmonics of the actuating torques (forces) necessary for tracking trajectories that are uniformly distributed within a representative task space are determined, and used as a measure of the potential for vibrational excitation during motion. The manipulators are kinematically and dynamically equivalent. From the vibration and control points of view, manipulator types that do not demand high frequency actuating torque harmonics are more desirable, since the natural modes of vibration of mechanical systems are most likely to be excited by the higher harmonics of the actuating torques, and because of practical dynamic response limitations of all mechanical systems. As examples, plane two and three degrees-of-freedom manipulators constructed with revolute and prismatic joints are studied. Numerical calculations of the aforementioned and the total expected (average) energy input and the corresponding variances are presented for the two degrees-of-freedom manipulators. A number of points of interest are discussed.

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