Control of Flexible Payloads Grasped by Actuated Grippers Undergoing Large Rigid-Body Motions: Part II — Controllability and Observability

2002 ◽  
Author(s):  
Edward J. Park ◽  
James K. Mills
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Time Scale ◽  
Body Motion ◽  
Deformation Control ◽  
Scale Modeling ◽  
Fixed Interface ◽  
Controllability And Observability ◽  
Scale Behavior ◽  
Selection Of

Part I of this work models the dynamics of a flexible payload grasped by an actuated gripper undergoing large rigid body motion by a robotic manipulator. In Part II, the controllability and observability conditions of the system are discussed. In Part I, the dynamic model of the actuated flexible payload is derived using the component mode synthesis (CMS) method with addition of actuator constraint, fixed-interface vibration and quasi-static modes. Here, the two-time scale modeling (TSM) technique is employed taking advantage of the two-time scale behavior between the quasi-static modes and vibration modes in the dynamic model. Due to the complexity of the resulting system, the controllability and observability conditions are not trivial. Hence, the controllability and observability study addressed herein becomes essential in showing the advantages of using the CMS and TSM techniques in control system design for the problem. A simulation example demonstrates that simultaneous vibration and quasi-static deformation control is achievable by proper selection of each type of modes.

Control of Flexible Payloads Grasped by Actuated Grippers Undergoing Large Rigid-Body Motions: Part I — Dynamics

2002 ◽  
Author(s):  
Edward J. Park ◽  
James K. Mills
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Time Scale ◽  
Normal Modes ◽  
Body Motion ◽  
Actuator Dynamics ◽  
Scale Modeling ◽  
Fixed Interface ◽  
The Given ◽  
System Order

This paper is Part I of a preliminary study to simultaneously control vibration and static shape deformation in flexible payloads. In Part I, the dynamics of a flexible payload grasped by an actuated gripper, which is attached to a rigid link robotic manipulator, is investigated using the component mode synthesis (CMS) method. Robot and actuator dynamics are also added to the system dynamic model to fully define the rigid body motion and elastic motion of the flexible payload. The CMS method is employed to explicitly model the coupling between the payload and actuators, and to reduce the system order. With the addition of fixed-interface quasi-static modes to fixed-interface vibration normal modes and actuator constraint modes an improved component mode representation is defined. Here, it is found that the inclusion of quasi-static modes in the CMS formulation results in increased ac curacy for simulation of dynamic behaviour of flexible payloads subject to both gravity and robot motion induced forces. Numerical examples are presented to demonstrate the effectiveness of the new component mode representation for the given robotics problem. In Part II [9], the two-time scale modeling (TSM) technique is used taking advantage of two-time scale behavior between the quasi-static modes and vibration modes in the dynamic model.

Using Dual Cam Tracks for High Speed Rigid Body Motion

1998 ◽  
Author(s):  
Clay Cooper ◽  
Stephen Derby
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Transfer Rates ◽  
Track System ◽  
Selection Of

Abstract Rigid Body Motion has long been one of the standard problems for kinematicians. For high speed transfer rates, an industrial example of using a dual cam track system to achieve better performance is documented. The dual track establishes both a positional and orientational location of the followers. The selection of this mechanism type is discussed.

A New Theoretical and Numerical Approach to Finite Rigid Body Rotations Based on Lie Group Theory

2013 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Elias Paraskevopoulos ◽  
Nikolaos Potosakis
Keyword(s):  
Rigid Body ◽  
Configuration Space ◽  
Differentiable Manifold ◽  
Numerical Approach ◽  
Body Motion ◽  
Strong Basis ◽  
Lie Group Theory ◽  
Large Rotations ◽  
Basic Characteristics ◽  
Selection Of

A systematic theoretical approach is presented first, in an effort to provide a complete and illuminating study on motion of a rigid body rotating about a fixed point. Since the configuration space of this motion is a differentiable manifold possessing group properties, this approach is based on some fundamental concepts of differential geometry. A key idea is the introduction of a canonical connection, matching the manifold and group properties of the configuration space. Next, following the selection of an appropriate metric, the dynamics is also carried over. The present approach is theoretically more demanding than the traditional treatments but brings substantial benefits. In particular, an elegant interpretation can be provided for all the quantities with fundamental importance in rigid body motion. It also leads to a correction of some misconceptions and geometrical inconsistencies in the field. Finally, it provides powerful insight and a strong basis for the development of efficient numerical techniques in problems involving large rotations. This is demonstrated by an example, including the basic characteristics of the class of systems examined.

Modeling the Dynamics of Five-Axis Machine Tool Using the Multibody Approach

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Hoai Nam Huynh ◽  
Yusuf Altintas
Keyword(s):  
Rigid Body ◽  
Machine Tool ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Performance ◽  
Body Motion ◽  
Proposed Model ◽  
Multibody Dynamic ◽  
Machining Operations ◽  
Five Axis

Abstract A systematic modeling of multibody dynamics of five-axis machine tools is presented in this article. The machine is divided into major subassemblies such as spindle, column, bed, tool changer, and longitudinal and rotary drives. The inertias and mass center of each subassembly are calculated from the design model. The subassemblies are connected with elastic springs and damping elements at contact joints to form the complete multibody dynamic model of the machine that considers the rigid body kinematics and structural vibrations of the machine at any point. The unknown elastic joint parameters are estimated from the experimental modal analysis of the machine tool. The resulting position-dependent multibody dynamic model has the minimal number of degrees-of-freedom that is equivalent to the number of measured modes, as opposed to thousands used in finite element models. The frequency response functions of the machine can be predicted at any posture of the five-axis machine, which are compared against the directly measured values to assess the validity of model. The proposed model can predict the combined rigid body motion and vibrations of the machine with computational efficiency, and hence, it can be used as a digital twin to simulate its dynamic performance in machining operations and tracking control tests of the servo drives.

scholarly journals Modeling Legged Microrobot Locomotion Based on Contact Dynamics and Vibration in Multiple Modes and Axes

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Jinhong Qu ◽  
Clark B. Teeple ◽  
Kenn R. Oldham
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Contact Dynamics ◽  
Body Motion ◽  
Small Scale ◽  
Robot Locomotion ◽  
Actuation Scheme ◽  
Dynamics And Vibration

A dynamic model is developed for small-scale robots with multiple high-frequency actuated compliant elastic legs and a rigid body. The motion of the small-scale robots results from dual-direction motion of piezoelectric actuators attached to the legs, with impact dynamics increasing robot locomotion complexity. A dynamic model is developed to describe the small-scale robot motion in the presence of variable properties of the underlying terrain. The dynamic model is derived from beam theory with appropriate boundary and loading conditions and considers each robot leg as a continuous structure moving in two directions. Robot body motion is modeled in up to five degrees-of-freedom (DOF) using a rigid body approximation for the central robot chassis. Individual modes of the resulting multimode robot are treated as second-order linear systems. The dynamic model is tested with two different centimeter-scale robot prototypes having an analogous actuation scheme to millimeter-scale microrobots. In accounting for the interaction between the robot and ground, a dynamic model using the first two modes of each leg shows good agreement with experimental results for the centimeter-scale prototypes, in terms of both magnitude and the trends in robot locomotion with respect to actuation conditions.

A Velocity Metric for Rigid-Body Planar Motion

2010 ◽  
Author(s):  
Joseph M. Schimmels ◽  
Luis E. Criales
Keyword(s):  
Rigid Body ◽  
Average Distance ◽  
The Body ◽  
Body Motion ◽  
Length Scale ◽  
Translational Velocity ◽  
Body Velocity ◽  
Assembly Problem ◽  
Instantaneous Center ◽  
Selection Of

A planar rigid-body velocity metric based on the instantaneous velocity of all particles that constitute a rigid body is developed. A measure based on the discrepancy in the translational velocity at each particle for two different planar twists is introduced. The calculation of the measure is simplified to the calculation of the product of: 1) the discrepancy in angular velocity, and 2) the average distance of the body from the instantaneous center associated with the twist discrepancy. It is shown that this measure satisfies the mathematical requirements of a metric and is physically consistent. It does not depend on either the selection of length scale or the frames used to describe the body motion. Although the metric does depend on body geometry, it can be calculated efficiently using body decomposition. An example demonstrating the application of the metric to an assembly problem is presented.

Dynamic Response of Composite Pressure Vessels to Inertia Loads

1991 ◽  
Vol 113 (1) ◽  
pp. 86-91
Author(s):  
J. C. Prucz ◽  
J. D’Acquisto ◽  
J. E. Smith
Keyword(s):  
Rigid Body ◽  
Combustion Engine ◽  
Pressure Vessels ◽  
Body Motion ◽  
Connecting Rod ◽  
Filament Wound ◽  
Potential Benefits ◽  
Rigid Body Motions ◽  
Crank Mechanism ◽  
Selection Of

A new analytical model has been developed in order to investigate the potential benefits of using fiber-reinforced composites in pressure vessels that undergo rigid-body motions. The model consists of a quasi-static lamination analysis of a cylindrical, filament-wound, pressure vessel, combined with an elastodynamic analysis that accounts for the coupling effects between its rigid-body motion and its elastic deformations. The particular type of motion investigated in this paper is that of an oil-pressurized, tubular connecting rod in a slider-crank mechanism of an internal combustion engine. A comprehensive parametric study has been focused on the maximum wall stresses induced in such a rod by the combined effect of internal pressure and inertia loads associated with its motion. The numerical results illustrate potential ways to reduce these stresses by appropriate selection of material systems, lay-up configurations and geometric parameters.

scholarly journals Dynamic Model and Fault Feature Research of Dual-Rotor System with Bearing Pedestal Looseness

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Nanfei Wang ◽  
Hongzhi Xu ◽  
Dongxiang Jiang
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Dynamic Model ◽  
Rigid Motion ◽  
Rotor System ◽  
Experimental Results ◽  
Body Motion ◽  
Combination Frequency ◽  
Recovery Coefficient ◽  
Vibration Displacement

The paper presents a finite element model of dual-rotor system with pedestal looseness stemming from loosened bolts. Dynamic model including bearing pedestal looseness is established based on the dual-rotor test rig. Three-degree-of-freedom (DOF) planar rigid motion of loose bearing pedestal is fully considered and collision recovery coefficient is also introduced in the model. Based on the Timoshenko beam elements, using the finite element method, rigid body kinematics, and the Newmark-βalgorithm for numerical simulation, dynamic characteristics of the inner and outer rotors and the bearing pedestal plane rigid body motion under bearing pedestal looseness condition are studied. Meanwhile, the looseness experiments under two different speed combinations are carried out, and the experimental results are basically the same. The simulation results are compared with the experimental results, indicating that vibration displacement waveforms of loosened rotor have “clipping” phenomenon. When the bearing pedestal looseness fault occurs, the inner and outer rotors vibration spectrum not only contains the difference and sum frequency of the two rotors’ fundamental frequency but also contains2Xand3Xcomponent of rotor with loosened support, and so forth; low frequency spectrum is more, containing dividing component, and so forth; the rotor displacement spectrums also contain fewer combination frequency components, and so forth; when one side of the inner rotor bearing pedestal is loosened, the inner rotor axis trajectory is drawn into similar-ellipse shape.

Dynamic Model of the Piston-Ring Assembly Using Curved Beam Finite Elements

2011 ◽  
Author(s):  
Mohannad Hakeem ◽  
Nabil G. Chalhoub ◽  
Peter Schihl
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Piston Ring ◽  
Translational Motion ◽  
Total Duration ◽  
Variable Structure ◽  
Body Motion ◽  
Curved Beam ◽  
Connecting Rod

A dynamic model for the crankshaft/connecting-rod/piston-assembly for a single cylinder engine is developed. The model considers the rigid body motion of the crank-slider mechanism including the piston secondary motions such as the piston-slap and piston-tilting. The formulation considers the ring to have three rigid body degrees of freedom in addition to its longitudinal and in-plane transverse deformations. The structural flexibility terms are approximated by using curved beam finite element method. The dynamic model has a variable structure whereby the number of degrees of freedom depends on the piston-liner and piston-ring interactions. Its formulation does not include frictional losses. The simulation results illustrate the piston secondary motions along with the ring tilting angles relative to the piston orientation for the total duration of the engine cycle. In addition, they exhibit the translational motion of the ring within the piston groove.

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