Lumped-Parameter Modeling of Visco-Elastically Coupled Rigid Bodies Using Clifford’s Biquaternions

2000 ◽  
Author(s):  
Ernest D. Fasse
Keyword(s):  
Computer Simulation ◽  
Rigid Bodies ◽  
Elastic Coupling ◽  
Potential Utility ◽  
Dual Quaternions ◽  
Lumped Parameter ◽  
Lumped Parameter Modeling

Abstract This work considers the problem of modeling visco-elastically coupled rigid bodies, with application to modeling and computer simulation of spatial, flexural mechanisms. A method of modeling visco-elastic coupling based on Clifford’s biquaternions (dual quaternions) is presented. The potential utility of the method is demonstrated by simulating the behavior of a complex spatial, flexural mechanism.

Application of screw theory to lumped-parameter modelling of elastically coupled rigid bodies

2002 ◽  
Vol 216 (1) ◽  
pp. 105-121 ◽  
Author(s):  
E D Fasse
Keyword(s):  
Computer Simulation ◽  
Screw Theory ◽  
Rigid Bodies ◽  
Potential Utility ◽  
Dual Number ◽  
Lumped Parameter ◽  
Modelling Methods

This work considers the problem of modelling elastically coupled rigid bodies, with application to modelling and computer simulation of spatial, flexural mechanisms. Two modelling methods are presented, both of which use elements of screw theory and dual number calculus. The potential utility of the methods is demonstrated by simulating the behaviour of a complex spatial, flexural mechanism.

scholarly journals Non-Linear Lumped-Parameter Modeling of Planar Multi-Link Manipulators with Highly Flexible Arms

Robotics ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 60 ◽  
Author(s):  
Ivan Giorgio ◽  
Dionisio Del Vescovo
Keyword(s):  
Control Strategy ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Chain Model ◽  
Joint Angles ◽  
Lumped Parameter ◽  
Bending Resistance ◽  
Parabolic Trajectory ◽  
Lumped Parameter Modeling ◽  
Flexible Arms

The problem of the trajectory-tracking and vibration control of highly flexible planar multi-links robot arms is investigated. We discretize the links according to the Hencky bar-chain model, which is an application of the lumped parameters techniques. In this approach, each link is considered as a kinematic chain of rigid bodies, and suitable springs are added in order to model bending resistance. The control strategy employed is based on an optimal input pre-shaping and a feedback of the joint angles to treat the effects of undesired disturbances. Some numerical examples are given to show the potentialities of the proposed control, and a comparison with a standard collocated Proportional-Derivative (PD) control strategy is performed. In particular, we study the cases of a linear and a parabolic trajectory with a polynomial time law chosen to minimize the onset of possible vibrations.

Lumped Parameter Modeling of a Magnetorheological Fluid Clutch

2006 ◽  
Author(s):  
John C. Ulicny ◽  
Daniel J. Klingenberg ◽  
Anthony L. Smith ◽  
Zongxuan Sun
Keyword(s):  
Mathematical Model ◽  
Physical Properties ◽  
Magnetorheological Fluid ◽  
Input Current ◽  
Fluid Composition ◽  
Fluid Temperature ◽  
Temperature Range ◽  
Lumped Parameter ◽  
Lumped Parameter Modeling ◽  
Fan Speed

A lumped-parameter mathematical model of an automotive magnetorheological (MR) fluid fan clutch was developed. This model is able to describe the average fluid temperature, average clutch temperature, and output fan speed as a function of time, input current, and fluid composition. The model also reproduces numerous features of fan operation observed experimentally and revealed a mechanism for some observed cases of hysteresis. However, it fails to capture certain other features which lead us to conclude that phenomena which are not included in the model, e.g., sedimentation and re-suspension, are important to the clutch behavior. In addition, the results indicate that certain physical properties need to be measured over a larger temperature range in order for the model to better predict the clutch behavior.

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