Mathematical modeling of the slip of a system of rigid bodies along a surface

1991 ◽  
Vol 27 (12) ◽  
pp. 1228-1234
Author(s):  
N. V. Nikitina
Keyword(s):  
Mathematical Modeling ◽  
Rigid Bodies ◽  
System Of Rigid Bodies

Improving Techniques in Statically Equivalent Serial Chain Modeling for Center of Mass Estimation

2014 ◽  
Author(s):  
Bingjue Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Center Of Mass ◽  
Original System ◽  
Rigid Bodies ◽  
Joint Angles ◽  
Practical Applications ◽  
Serial Chain ◽  
System Of Rigid Bodies ◽  
Final Development ◽  
Data Error ◽  
Insight Into

Any articulated system of rigid bodies defines a Statically Equivalent Serial Chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. A SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed. Second, the problem of generating a SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.

The Geometry of Virtual Work Dynamics in Screw Space

1992 ◽  
Vol 59 (2) ◽  
pp. 411-417 ◽  
Author(s):  
Steven Peterson
Keyword(s):  
Tangent Space ◽  
Screw Theory ◽  
Virtual Work ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Coordinate Space ◽  
Dynamical Equations ◽  
Least Action ◽  
System Of Rigid Bodies ◽  
Configuration Manifold

In this paper, screw theory is employed to develop a method for generating the dynamic equations of a system of rigid bodies. Exterior algebra is used to derive the structure of screw space from projective three space (homogeneous coordinate space). The dynamic equation formulation method is derived from the parametric form of the principle of least action, and it is shown that a set of screws exist which serves as a basis for the tangent space of the configuration manifold. Equations generated using this technique are analogs of Hamilton’s dynamical equations. The freedom screws defining the manifold’s tangent space are determined from the contact geometry of the joint using the virtual coefficient, which is developed from the principle of virtual work. This results in a method that eliminates all differentiation operations required by other virtual work techniques, producing a formulation method based solely on the geometry of the system of rigid bodies. The procedure is applied to the derivation of the dynamic equations for the first three links of the Stanford manipulator.

scholarly journals Experimental Investigation of the Painlevé Paradox in a Robotic System

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Zhen Zhao ◽  
Caishan Liu ◽  
Wei Ma ◽  
Bin Chen
Keyword(s):  
Contact Point ◽  
Tangential Velocity ◽  
Rigid Bodies ◽  
Robotic System ◽  
Experimental Results ◽  
Painlevé Paradox ◽  
Dynamical Behaviors ◽  
Tangential Impact ◽  
System Of Rigid Bodies ◽  
Approach Zero

This paper aims at experimentally investigating the dynamical behaviors when a system of rigid bodies undergoes so-called paradoxical situations. An experimental setup corresponding to the analytical model presented in our prior work Liu et al. [2007, “The Bouncing Motion Appearing in a Robotic System With Unilateral Constraint,” Nonlinear Dyn., 49(1–2), 217–232] is developed, in which a two-link robotic system comes into contact with a moving rail. The experimental results show that a tangential impact exists at the contact point and takes a peculiar property that well coincides with the maximum dissipation principle stated in the work of Moreau [1988, “Unilateral Contact and Dry Friction in Finite Freedom Dynamics,” Nonsmooth Mechanics and Applications, Springer-Verlag, Vienna, pp. 1–82] the relative tangential velocity of the contact point must immediately approach zero once a Painlevé paradox occurs. After the tangential impact, a bouncing motion may be excited and is influenced by the speed of the moving rail. We adopt the tangential impact rule presented by Liu et al. to determine the postimpact velocities of the system, and use an event-driven algorithm to perform numerical simulations. The qualitative comparisons between the numerical and experimental results are carried out and show good agreements. This study not only presents an experimental support for the shock assumption related to the problem of the Painlevé paradox, but can also find its applications in better understanding the instability phenomena appearing in robotic systems.

Identification and Significance of the First Structural Modes of Vibration of Two Wheeled Vehicles

2010 ◽  
Author(s):  
Alberto Doria ◽  
Luca Trombetta ◽  
Roberto Pegoraro
Keyword(s):  
Modal Analysis ◽  
Rigid Bodies ◽  
Elastic Behavior ◽  
Local Modes ◽  
System Of Rigid Bodies ◽  
Swing Arm ◽  
Modes Of Vibration ◽  
Small Set ◽  
Vehicle Chassis ◽  
Motorcycle Dynamics

In motorcycles and scooters the structural modes of vibration are important because they influence both vehicle’s comfort and vehicle’s stability and handling. Some researchers have shown that instabilities, which may occur when the vehicle is running (weave and wobble), are influenced by the modes of vibration, of the vehicle. At the Motorcycle Dynamics Research Group of Padova University many motorcycles have been tested with the method of modal analysis. The results of this research highlight that the whole motorcycle is a complex system that shows many kinds of modes of vibration: rigid modes, in which the structural components of the vehicle (chassis, fork, handlebars) behave as rigid bodies and deflection is given by tires and suspensions; local modes, in which deflection is concentrated in some subsystem of the vehicle (e.g. handlebars) and the rest of the motorcycle behaves as a system of rigid bodies; global modes with relevant deflection of the whole vehicle. This paper focuses on a specific issue, which is important for motorcycle design: the identifications of the frequencies of the first modes that show relevant deflection of the front fork and swing-arm. First, experimental equipment and testing methods are presented and discussed. Then the modal properties (natural frequencies, damping coefficients and modal shapes) of four motorcycles of different categories are presented, the characteristics of some modes are highlighted. Finally, the paper focuses on the identification of the frequencies that represent the borderline between rigid and elastic behavior of front fork and swing-arm. A method that requires the analysis of the characteristics of a small set of frequency response functions, without carrying out a long and expensive modal analysis of the whole vehicle, is presented. It is based on the properties of rigid modes (variation in vibration amplitude along a set of measurement points).

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