The Robotics, Biomechanics, and Dynamic Systems Laboratory 

Bouncing Bicycle 
Hybrid Dynamic Simulation

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 multipoint 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 rigidbody relationship between the postimpact 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 MultiPoint 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 rigidbody relationship between the postimpact velocities at each impact point. Adrian Rodriguez and Alan Bowling. Solution to Indeterminate MultiPoint 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 2745, August 2009. 

Download by Daniel Montrallo Flickinger 5/08/2009 
Normal Impact Forces 
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 2745, August 2009.  
Download by Daniel Montrallo Flickinger 7/08/2009 
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 postimpact tangential velocities. The noslip 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 postimpact 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 249261, March 2010.  
Download by Daniel Montrallo Flickinger 7/08/2009 
Optimized Coefficient of Friction 
Feasible Tangential Velocities and Coefficients of Friction 