Sir Robert Stawell Ball and methodologies of modern screw theory

2002 ◽  
Vol 216 (1) ◽  
pp. 1-11 ◽  
Author(s):  
H Lipkin ◽  
J Duffy
Keyword(s):  
Computational Geometry ◽  
Rigid Body ◽  
Lie Algebra ◽  
Screw Theory ◽  
Mechanical Design ◽  
Ball Screw ◽  
Dual Numbers ◽  
Body Dynamics ◽  
Rigid Body Mechanics ◽  
Multi Body

The theory of screws was largely developed by Sir Robert Stawell Ball over 100 years ago to investigate general problems in rigid body mechanics. Nowadays, screw theory is applied in many different but related forms including dual numbers, Plilcker coordinates and Lie algebra. An overview of these methodologies is presented along with a perspective on Ball. Screw theory has re-emerged after a hiatus to become an important tool in robot mechanics, mechanical design, computational geometry and multi-body dynamics.

Evaluation of Human Body Dynamical Behaviour During Handling Maneuvers and Crash Test Simulations Using Multi-Body Codes

2006 ◽  
Author(s):  
Francesco Braghin ◽  
Paolo Pennacchi ◽  
Edoardo Sabbioni
Keyword(s):  
Rigid Body ◽  
Human Body ◽  
Dynamical Behaviour ◽  
Crash Test ◽  
Frontal Crash ◽  
Race Car ◽  
Body Dynamics ◽  
Multi Body ◽  
Vehicle Chassis ◽  
Crash Tests

The dynamic behavior of the human body during race car maneuvers and frontal crash tests is analyzed in this paper. Both the vehicle and the human body have been modeled using the multi-body approach. Two commercial codes, BRG LifeMOD Biomechanics Modeler®, for the simulation of the human body dynamics, and MSC ADAMS/Car® for the modeling of the vehicle behavior, have been used for the purpose. Due to the impossibility of co-simulating, at first the accelerations on the driver’s chassis are determined using the vehicle’s multibody code and approximating the driver as a rigid body. Then, the calculated accelerations are applied to the vehicle chassis in the biomechanics code to assess the accelerations in various significant points on the driver.

Geometric Pseudospectral Method on Lie Group with Application to 3D Pendulum

2013 ◽  
Vol 756-759 ◽  
pp. 3021-3029
Author(s):  
Jie Li ◽  
Hong Lei An ◽  
Xue Qiang Gu ◽  
Hong Tao Xue
Keyword(s):  
Differential Equation ◽  
Rigid Body ◽  
Lie Algebra ◽  
Lie Group ◽  
Structural Characteristics ◽  
Pseudospectral Method ◽  
Rigid Body Dynamics ◽  
Equivariant Map ◽  
Body Dynamics

General pseudospectral method is extended to Lie group by virtue of equivariant map for solving rigid dynamics on Lie group. In particular, for the problem of structural characteristics of the dynamics system can not be conserved by using general pseudospectral method directly on Lie group, the differential equation evolving on the Lie group is transformed to an equivalent differential equation evolving on a Lie algebra on which general pseudospectral method is used, so that the numerical flow of rigid body dynamics is ensured to stay on Lie group. Furthermore, structural conservativeness and numerical stabilities of this method are validated and analyzed by simulation on a 3D pendulum in comparison with using pseudospectral method directly on Lie group.

The Multi-Body Dynamics Contact Simulation on Transmission Gears

2014 ◽  
Vol 989-994 ◽  
pp. 3037-3040
Author(s):  
Xiao He Deng
Keyword(s):  
Fourier Transform ◽  
Rigid Body ◽  
Simulation Model ◽  
Simulation Analysis ◽  
Rigid Body Dynamics ◽  
Gear Dynamics ◽  
Body Dynamics ◽  
Multi Body ◽  
Shift Gears

Based on the theory of gear dynamics and contact, the paper uses multi-rigid-body dynamics software ADAMS to build transmission simulation model. The model takes the highest shift gears of a transmission as objects to finish gear meshing simulation analysis. The corresponding meshing force and its Fourier transform results are acquired based on the analysis to get the transmission gears meshing properties.

DYNAMICS MODELING AND SIMULATION OF A KIND OF WHEELED HUMANOID ROBOT BASED ON SCREW THEORY

2012 ◽  
Vol 09 (04) ◽  
pp. 1250029 ◽  
Author(s):  
JINGGUO WANG ◽  
YANGMIN LI
Keyword(s):  
Humanoid Robot ◽  
Screw Theory ◽  
Kinematics And Dynamics ◽  
Variation Principle ◽  
Dynamics Modeling ◽  
Modeling Methodology ◽  
Body Dynamics ◽  
Simulation Results ◽  
Multi Body ◽  
The Relationship

Based on the screw theory and Lie group notations, this paper presents a modeling method for a kind of wheeled humanoid robot whose upper human-like body is mounted on the top of a mobile platform with three wheels. By combining the reciprocal product of the twist and wrench with Jourdain variation principle, a general formulation method is proposed to model the whole system's dynamics that represents directly the relationship between the input and the resultant external and inertial wrench. Both the system kinematics and dynamics are derived carefully. The simulations are made to verify the proposed modeling methodology and the simulation results are also compared with the results obtained from the multi-body dynamics software.

Explicit Poincaré equations of motion for general constrained systems. Part II. Applications to multi-body dynamics and nonlinear control

2007 ◽  
Vol 463 (2082) ◽  
pp. 1435-1446 ◽  
Author(s):  
Firdaus E Udwadia ◽  
Phailaung Phohomsiri
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Constrained Systems ◽  
The Third ◽  
Highly Nonlinear ◽  
Body Dynamics ◽  
Multi Body

The power of the new equations of motion developed in part I of this paper is illustrated using three examples from multi-body dynamics. The first two examples deal with the problem of accurately controlling the orientation of a rigid body, while the third example deals with the synchronization of two rigid bodies so that their relative orientations are ‘locked’ through prescribed dynamical relationships. The ease, simplicity and accuracy with which control of such highly nonlinear systems is achieved are demonstrated.

Research on MFBD Modeling Method for a Gantry Machining Center Beam Components

2011 ◽  
Vol 188 ◽  
pp. 487-492 ◽  
Author(s):  
Q.J. Yang ◽  
D.N. Li ◽  
L.L. Kong ◽  
K. Li
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
High Speed ◽  
Modeling Method ◽  
Ball Screw ◽  
Machining Processes ◽  
Element Analysis ◽  
Machining Center ◽  
Body Dynamics ◽  
Multi Body

In modern machining processes, Gantry Machining Center is one of the most important machine tools. Moreover, beam components directly relate to the overall performance. From multi-body simulation (MBS) and finite element analysis (FEA) respectively, the paper discusses current state of the multi-body dynamics modelling of the machine tool components in domestic and overseas. In this paper, We adopt a method, the multi-flexible body dynamics(MFBD) modeling method for machine tool transmission components (linear guidance and ball screw drives) in software Recurdyn, to create the conditions for MFBD simulation analysis of the beam components system. Much more, it provides a way of MFBD modelling for machine tools components in both the high-speed and high-performance.

scholarly journals Geometric Pseudospectral Method on SE(3) for Rigid-Body Dynamics with Application to Aircraft

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Jie Li ◽  
Honglei An ◽  
Huayong Zhu ◽  
Lincheng Shen ◽  
Bin Fang
Keyword(s):  
Rigid Body ◽  
Lie Algebra ◽  
Lie Group ◽  
Pseudospectral Method ◽  
Velocity Model ◽  
Rigid Body Dynamics ◽  
Dynamics Simulation ◽  
Configuration Model ◽  
Body Dynamics ◽  
And Control

General pseudospectral method is extended to the special Euclidean group SE(3) by virtue of equivariant map for rigid-body dynamics of the aircraft. On SE(3), a complete left invariant rigid-body dynamics model of the aircraft in body-fixed frame is established, including configuration model and velocity model. For the left invariance of the configuration model, equivalent Lie algebra equation corresponding to the configuration equation is derived based on the left-trivialized tangent of local coordinate map, and the top eight orders truncated Magnus series expansion with its coefficients of the solution of the equivalent Lie algebra equation are given. A numerical method called geometric pseudospectral method is developed, which, respectively, computes configurations and velocities at the collocation points and the endpoint based on two different collocation strategies. Through numerical tests on a free-floating rigid-body dynamics compared with several same order classical methods in Euclidean space and Lie group, it is found that the proposed method has higher accuracy, satisfying computational efficiency, stable Lie group structural conservativeness. Finally, how to apply the previous discretization scheme to rigid-body dynamics simulation and control of the aircraft is illustrated.

TWO PROBLEMS OF RIGID BODY MECHANICS

2016 ◽  
Vol 47 (7) ◽  
pp. 775-782
Author(s):  
Vladimir Alekseevich Shvilkin
Keyword(s):  
Rigid Body ◽  
Rigid Body Mechanics
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