Effects of Payload on the Vibrational Excitation of Robot Manipulators During Motion

1994 ◽  
Author(s):  
Q. Tu ◽  
J. Rastegar
Keyword(s):  
Vibrational Excitation ◽  
Open Loop ◽  
Point Of View ◽  
End Effector ◽  
Harmonic Content ◽  
Mass Size ◽  
Payload Mass ◽  
Trajectory Pattern ◽  
Point To Point ◽  
Trajectory Pattern Method

Abstract The effects of payload mass, size, and end-effector holding location on the vibrational excitation of manipulators during motion are determined based on a new method, referred to as the trajectory pattern method. This is accomplished by examining the harmonic content of the actuating torques (forces) required for open-loop tracking of a selected trajectory pattern, the relative amplitude of each harmonic, and the energy input to the system by each harmonic. The simplest possible trajectory pattern for point to point motions with zero end point acceleration and jerk is employed as the basis for this study. It is shown that the amplitude of each harmonic is affected differently by the addition of the payload. The amplitudes change depending on the direction of motion and the location of the path of motion within the workspace of the manipulator. The harmonic content of the required actuating torques are not affected. The study provides information for planning paths of motion and synthesizing trajectories that are from the vibration point of view less sensitive to the payload. As an example, the effects of payload on a plane 2R manipulator are studied.

Trajectory Pattern Method Based Trajectory Synthesis and Inverse Dynamics Formulation for Minimal Vibrational Excitation for Flexible Structures

1996 ◽  
Author(s):  
Q. Tu ◽  
J. Rastegar
Keyword(s):  
Inverse Dynamics ◽  
Vibrational Excitation ◽  
Flexible Structures ◽  
Frequency Component ◽  
High Frequency Component ◽  
Flexible Beam ◽  
Dynamics Model ◽  
Trajectory Pattern ◽  
Point To Point ◽  
Trajectory Pattern Method

Abstract A new approach to trajectory synthesis and formulation of the inverse dynamics model of flexible structures for point to point motions with minimal high frequency component of the actuating torques (forces) is presented. Trajectories are synthesized such that the flexible structure comes to rest undeformed at the completion of motion. The developed method is based on the Trajectory Pattern Method. In this approach, an appropriate trajectory pattern is selected and described in parametric form. The inverse dynamics model of the system is formulated in terms of the trajectory parameters. The trajectory patterns used are in terms of a number of basic sinusoidal time functions and their harmonics. The basic frequencies are selected such that the harmonics appearing in the actuating torques do not excite the natural modes of vibration of the system. For each motion, the trajectory parameters are determined for minimal amplitudes of the higher actuating torque harmonics, noting that from the vibration and control points of view, such trajectories are more desirable. The higher harmonics refers to the harmonics of the actuating torques with frequencies above the highest trajectory harmonic frequency. As an example, a flexible beam undergoing large displacements and rotations in a plane is considered. The effectiveness of the approach is illustrated by an example.

scholarly journals Low-harmonic trajectory synthesis using trajectory pattern method (TPM) for high-speed and high-precision machinery

2021 ◽  
Vol 12 (2) ◽  
pp. 913-922
Author(s):  
Hao Li ◽  
Jahangir Rastegar ◽  
Baosheng Wang
Keyword(s):  
Dynamic Response ◽  
Fundamental Frequency ◽  
High Frequency ◽  
High Speed ◽  
Harmonic Content ◽  
Modes Of Vibration ◽  
Trajectory Pattern ◽  
Trajectory Pattern Method ◽  
High Frequency Harmonic ◽  
Frequency Harmonic

Abstract. In high-speed and high-precision machinery, trajectories with high-frequency harmonic content are one of the main sources of reduction of operational precision. Trajectories with high-frequency harmonic content generally demand even higher-harmonic actuating forces/torques due to the nonlinear dynamics of such systems, which may excite natural modes of vibration of the system and/or be beyond the dynamic response limitation of the actuation devices. In this paper, a global interpolation algorithm that uses the trajectory pattern method (TPM) for synthesizing low-harmonic trajectories is presented. The trajectory synthesis with the TPM is performed with a prescribed fundamental frequency and continuous jounce boundary condition, which would minimize the number of high-harmonic components in the required actuation forces/torques and avoid excitation of the system modes of vibration. The minimal curvature variation energy method, Lagrange multiplier method, and contour error control are used to obtain smooth kinematic profiles and satisfy the trajectory accuracy requirements. As an example, trajectory patterns that consist of a fundamental frequency sinusoidal time function and its first three harmonics are used to synthesize the desired trajectories for a selected dynamic system. The synthesized trajectories are shown to cause minimal system vibration during its operation. A comparison with a commonly used trajectory synthesis method clearly shows the superiority of the developed TPM-based approach in reducing vibration and demand on the actuator dynamic response, thereby allowing the system to operate at higher speeds and precision.

Studies on Isotropy of Planar 5-Bar Linkages

2004 ◽  
Author(s):  
C. Amarnath ◽  
K. N. Umesh
Keyword(s):  
Geometric Approach ◽  
Geometrical Approach ◽  
End Effector ◽  
Isotropic Point ◽  
Important Requirement ◽  
Point To Point

The ability to move at reasonable ease in all directions is an important requirement in the design of manipulators. The degree of ease of mobility varies from point to point in the workspace of the manipulator’s end effector. Maximum ease of mobility is obtained at an isotropic point, and the minimum occurs at singularities. An attempt has been made here to use a geometric approach for determining the isotropic points in the workspace of planar 5-bar linkages. The geometrical approach leads to interesting observations on the location of isotropic points in the workspace. The procedure also yields a technique for the synthesis of 5-bar linkages and associated coupler points exhibiting isotropic behaviour. Additionally it has been shown that coupler points exhibiting isotropic mobility occur in pairs.

Kinematic interpretation in the prestack depth‐migrated domain

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1226-1237 ◽  
Author(s):  
Irina Apostoiu‐Marin ◽  
Andreas Ehinger
Keyword(s):  
Signal To Noise Ratio ◽  
Velocity Model ◽  
Point Of View ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Models ◽  
Time Domain Data ◽  
And Migration ◽  
Point To Point ◽  
Homogeneous Media

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.

On the Inherent Characteristics of the Dynamics of Robot Manipulators

1991 ◽  
Author(s):  
Q. Tu ◽  
J. Rastegar
Keyword(s):  
Path Length ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Robot Manipulators ◽  
Control Point ◽  
Coordinate Space ◽  
Relative Significance ◽  
Harmonic Content ◽  
Trajectory Pattern ◽  
Dynamics Models

Abstract The inherent characteristics of the (nonlinear) dynamics of robot manipulators are studied. The study is based on a new method, referred to as the trajectory pattern method. The inverse dynamics models of the manipulator are divided into classes of inverse dynamics models, each corresponding to a different trajectory pattern. For each trajectory pattern, the structure of the resulting inverse dynamics model is fixed and is used to study the characteristics of the dynamics of the manipulator by examining the harmonic content of the required actuation torques (forces) and the relative significance of each harmonic. The harmonic content of the actuating torques is shown to be a function of the path length in the joint coordinate space and the harmonic content of the selected trajectory pattern, but is independent of the number of degrees-of-freedom of the manipulator. The relative contribution of each harmonic is a function of the path length, direction of motion, the position of the path of motion within the workspace of the manipulator, and the magnitude of the fundamental frequency. The study provides a systematic approach to path and trajectory planning from the vibration control point of view. As an example, the characteristics of the dynamics of a spatial 3R manipulator is studied for motions with two different path lengths, starting from a specified point and extending in different directions.

A Statically Balanced Gough/Stewart-Type Platform: Conception, Design, and Simulation

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Marco Carricato ◽  
Clément Gosselin
Keyword(s):  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Theoretical Point ◽  
Constant Force ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Neutral Equilibrium ◽  
The Difference ◽  
Elastic Elements

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical designs of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in equilibrium in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. The performance of a study prototype is simulated via a model in both static and dynamic conditions, in order to prove the feasibility of the proposed design. The effects of imperfect balancing, due to the difference between the payload inertial characteristics and the theoretical/nominal ones, are investigated. Under a theoretical point of view, formal and novel derivations are provided of the necessary and sufficient conditions allowing (i) a body arbitrarily rotating in space to rest in neutral equilibrium under the action of general constant-force generators, (ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy, and (iii) a leg of a Gough/Stewart-type manipulator to operate as a constant-force generator.

Optimal Simultaneous Kinematic, Dynamic and Control Design of High Performance Manipulators Based on Trajectory Pattern Method

1998 ◽  
Author(s):  
J. Rastegar ◽  
L. Liu ◽  
M. Mattice
Keyword(s):  
High Speed ◽  
High Performance ◽  
Optimality Criterion ◽  
Control Design ◽  
Tracking Errors ◽  
Motion Patterns ◽  
Trajectory Pattern ◽  
And Control ◽  
Velocity Tracking ◽  
Trajectory Pattern Method

Abstract An optimal simultaneous kinematic, dynamic and control design approach is proposed for high performance computer controlled machines such as robot manipulators. The approach is based on the Trajectory Pattern Method (TPM) and a fundamentally new design philosophy that such machines in general and ultra-high performance machines in particular must only be designed to perform a class or classes of motions effectively. In the proposed approach, given the structure of the manipulator, its kinematic, dynamic and control parameters are optimized simultaneously with the parameters that describe the selected trajectory pattern. In the example presented in this paper, a weighted sum of the norms of the higher harmonics appearing in the actuating torques and the integral of the position and velocity tracking errors are used to form the optimality criterion. The selected optimality criterion should yield a system that is optimally designed to accurately follow the specified trajectory at high speed. Other objective functions can be readily formulated to synthesize systems for optimal performance. The potentials of the developed method and its implementation for generally defined motion patterns are discussed.

Analytic Geometric Design of Spatial R-R Robot Manipulators

2000 ◽  
Author(s):  
Constantinos Mavroidis ◽  
Munshi Alam ◽  
Eric Lee
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Open Loop ◽  
Geometric Design ◽  
Sixth Order ◽  
Design Parameters ◽  
End Effector ◽  
Revolute Joints ◽  
Order Polynomial ◽  
Spatial Locations

Abstract This paper studies the geometric design of spatial two degrees of freedom, open loop robot manipulators with revolute joints that perform tasks, which require the positioning of the end-effector in three spatial locations. This research is important in situations where a robotic manipulator or mechanism with a small number of joint degrees of freedom is designed to perform higher degree of freedom end-effector tasks. The loop-closure geometric equations provide eighteen design equations in eighteen unknowns. Polynomial Elimination techniques are used to solve these equations and obtain the manipulator Denavit and Hartenberg parameters. A sixth order polynomial is obtained in one of the design parameters. Only two of the six roots of the polynomial are real and they correspond to two different robot manipulators that can reach the desired end-effector poses.

scholarly journals Electromagnetic Radiation from the Geometrical Point of View

2018 ◽  
Vol 186 ◽  
pp. 01002
Author(s):  
Divakov Dmitriy ◽  
Malykh Mikhail ◽  
Tiutiunnik Anastasiia
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Radiation ◽  
Coordinate System ◽  
Maxwell's Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Point Of View ◽  
Curvilinear Coordinates ◽  
Point To Point ◽  
The Relationship

The article describes the relationship between the solutions of Maxwell's equations which can be considered at least locally as plane waves and the curvilinear coordinates of geometrical optics. We introduce phase-ray coordinate system for any electromagnetic field if vectors E and H are orthogonal to each other and their directions do not change with time t, but may vary from point to point in the domain G.

scholarly journals Rest-to-Rest Motion of an Experimental Flexible Structure Subject to Friction: Linear Programming Approach

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Rajaey Kased ◽  
Tarunraj Singh
Keyword(s):  
Linear Programming ◽  
Controller Design ◽  
Open Loop ◽  
Programming Approach ◽  
Pulse Control ◽  
Test Bed ◽  
Residual Vibration ◽  
Linear Programming Approach ◽  
Point To Point ◽  
Harmonic System

A linear programming approach designed to eliminate the residual vibration of the two-mass harmonic system subject to friction and undergoing a point-to-point maneuver is proposed and implemented on an experimental test bed. Techniques for design of positive pulse control profiles for nonrobust and robust open loop controller design are explored, where the positive pulses initiate motion and the friction force brings the system to rest. It is shown that consistent results can be obtained from experiments and the robustness against frequency uncertainty results in the reduction in residual vibration as well as steady-state error.

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