The Robotics, Biomechanics, and Dynamic Systems Laboratory

Planar Bicycle
Bouncing Bicycle

Hybrid Dynamic Simulation
Mahdi Haghshenas-Jaryani, Adrian Rodriguez



The simulation of multiple simultaneous impacts and contacts is still an open problem in multibody dynamics. Here a discrete algebraic method is used to model hard impacts, those that involve negligeable surface interaction. This work models contact and impacts with sticking, slipping, and rebound, with a energetic coefficient of restitution to ensure energy consistency. Several aspects of this problem had to be addressed in order to arrive at the simulations shown below, the details of which are dicussed in the papers on the previous page. The simulations were implemented using Matlab's ode45.m.


Videos

    by Adrian Rodriguez     2/8/2012
Rocking Block
This video shows a block falling and hitting a hard surface. The phenomena of interest involves the transfer of energy between two points on a block, one in contact and one experiencing impact. Impact is associated with an abrupt change in velocity, while contact is assumed to be a long term interaction between surfaces. In this simulation, When a point impacts the surface it sticks to it, the coefficient of restitution equals zero; however, a point in contact is free separate fron the surface. This type of simulation has been pursued by other researchers in relation to investigating the effects of earthquakes on buildings. This work presents a new approach to that type of simulation.

Adrian Rodriguez and Alan Bowling. Solution to indeterminate multi-point impact with frictional contact using constraints. Multibody System Dynamics. Accepted for publication.

    by Adrian Rodriguez     10/14/2011
3D ball Impacting a Corner
This video shows a 3D ball impacting a corner. The ball impacts all three surfaces simultaneously and sticking and slipping at the impact points is considered in the simulation. The three simultaneous impacts yield a model that is indeterminate with respect to the impact forces. These forces are resolved by enforcing the rigid-body relationship between the post-impact velocities at each impact point. The red asterisks on the ball indicate the three simultaneous impact points.

Adrian Rodriguez and Alan Bowling. Solution to Indeterminate Multi-Point Impact with Frictional Contact Using Constraints. Multibody System Dynamics. Accepted for publication.

    by Adrian Rodriguez     10/14/2011
2D ball Impacting a Corner
This video shows a 2D ball impacting a corner. The ball impacts both surfaces simultaneously and sticking and slipping at the impact points is considered in the simulation. The simultaneous impacts yield a planar model that is indeterminate with respect to the impact forces. These forces are resolved by enforcing the rigid-body relationship between the post-impact velocities at each impact point.

Adrian Rodriguez and Alan Bowling. Solution to Indeterminate Multi-Point Impact with Frictional Contact Using Constraints. Multibody System Dynamics. Accepted for publication.
A planar bicycle is dropped on a hard flat surface. The focus of this study was to examine the use of the energy modifying coefficient of restitution. The bicycle is given and initial velocity after which it impacts the surface, bounces, and eventually comes to rest. The coefficient of restitution for this simulation is less than one. The plot of normal impact forces shows the constant normal force after the bicycle is rolling on the surface as expected. The plot of energy consistency shows the time history of the total energy with and without the use of the energy modifying coefficient of restitution. In the unmodified case, impact with the surface actually adds energy into the system, a phenomena that may not be realistic. The use of the energy modifying coefficient of restitution prevents these energy gains allowing a more realistic simulation.

Alan Bowling, Daniel Montrallo Flickinger, and Sean Harmeyer. Energetically consistent simulation of simultaneous impacts and contacts for multibody systems with friction. Multibody System Dynamics, vol. 22, no. 1, pages 27-45, August 2009.

Download     by Daniel Montrallo Flickinger     5/08/2009
Contact forces
Normal Impact Forces
Energy Comparison
Energy Consistency
The bicycle is given ellipsoid wheels, and dropped with no initial velocity. The focus of this study was examination of the feasible coefficients of friction for oblique impacts. Thus the results of this simulation are meant to be compared with those in the next simulation. The coefficient of restitution is less than one. The spikes in the plot show that in most of the impacts the impact point sticks to the surface; the lower coefficient of friction indicates slipping of the impact point.

Alan Bowling, Daniel Montrallo Flickinger, and Sean Harmeyer. Energetically consistent simulation of simultaneous impacts and contacts for multibody systems with friction. Multibody System Dynamics, vol. 22, no. 1, pages 27-45, August 2009.

Download     by Daniel Montrallo Flickinger     7/08/2009
Coefficient of Friction
Coefficient of Friction
The angle of the wedge is increased to 45°, resulting in oblique impacts. The focus of this study was examination of the feasible coefficients of friction for oblique impacts. Again the coefficient of restitution is less than one. In this case the bicycle falls down the slope picking up energy as it falls faster and further. The steeper slope causes most of the impact points to slip, as one would expect. Slipping and sticking are investigated by examining the feasible regions for the coefficients of friction and the post-impact tangential velocities. The no-slip condition is combined with the complentarity conditions and the constraint that the normal impulse must be positive in order to obtain the feasible region. These constraints are implemented as an optimization which finds the post-impact tangential velocities. The plot shows the feasible region for the first impact which shows that sticking is infeasible. More discussion of this plot is given in the papers on the previous page.

Daniel Montrallo Flickinger and Alan Bowling. Simultaneous oblique impacts and contacts in multibody systems with friction. Multibody System Dynamics, vol. 23, no. 3, pages 249-261, March 2010.

Download     by Daniel Montrallo Flickinger     7/08/2009
Coefficient of Friction
Optimized Coefficient of Friction
Velocity Optimization
Feasible Tangential Velocities and Coefficients of Friction


Links

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last updated July 30, 2009