14
D. B. Marghitu and D. Cojocaru
An elasto-plastic contact law was proposed by Yigit for modeling the impact of
a single flexible link [3, 4]. The contact law allows continuous transition between
contact and non-contact phases and is capable of predicting impact force histories.
Marghitu and Hurmuzlu introduced a finite number of vibration modes to take
into account the vibrational effect for the impact of a single straight bar [5]. Effects
such as multicollisions, slip reversal, local vortex vector, and different configurations
were accommodated automatically.
The chain reaction from impact on coaxial multibody systems was studied by
Stronge [6]. Strong studied three spheres connected by springs to analyze the external
impact. The generated reaction force depends on the contact compliance and the mass
of the adjacent spheres.
The planar collision of rigid bodies with the friction between the bodies was
studied by Brach [7–9]. The general equations of impulse and momentum were
used. The effect of the moment impulse on the angular velocities was taken into
account through the use of a moment coefficient of restitution.
Kane and Levinson [10, 11] considered the generalized impulse and momentum equations for impact with friction. The impact equations include the generalized speeds before and after the impact. The system of equations was solved with
two assumptions involving the velocity of separation and the normal and tangential
impulse.
The planar body collisions with friction were studied by Wang and Mason [12].
Routh’s graphical method was employed to analyze the frictional impact. Poisson’s
and Newton’s methods were used for the impact analytical expressions. They show
that Poisson’s hypothesis does not violate energy conservation principles, while Newton’s coefficient of restitution is not always correct.
Johansson and Klarbring developed an algorithm for rigid body impact with friction [13]. The impenetrability condition and Coulomb’s law of friction are formulated as equations and solved together with the equations of motion using Newton’s
method. The impact process is described by the coefficient of friction, the coefficient
of restitution, and a new introduced coefficient of tangential restitution. The new
coefficient is determined experimentally.
As it can be noticed from the previous literature, most of the cases involved
impacts with Coulomb friction. In this study, during the impact a friction force based
on Benson model is employed.
2 Mathematical Model
2.1 Kinematics
Figure 1 is a schematic representation of a kinematic chain with two links 1 and 2. The
mass center of the link i is at C i , i = 1, 2. The dimensions are OC 1 = C 1 A = L 1
and AC 2 = C 2 T = L 2 . The “fixed” Newtonian reference frame (0), RF0, has the
D. B. Marghitu and D. Cojocaru
An elasto-plastic contact law was proposed by Yigit for modeling the impact of
a single flexible link [3, 4]. The contact law allows continuous transition between
contact and non-contact phases and is capable of predicting impact force histories.
Marghitu and Hurmuzlu introduced a finite number of vibration modes to take
into account the vibrational effect for the impact of a single straight bar [5]. Effects
such as multicollisions, slip reversal, local vortex vector, and different configurations
were accommodated automatically.
The chain reaction from impact on coaxial multibody systems was studied by
Stronge [6]. Strong studied three spheres connected by springs to analyze the external
impact. The generated reaction force depends on the contact compliance and the mass
of the adjacent spheres.
The planar collision of rigid bodies with the friction between the bodies was
studied by Brach [7–9]. The general equations of impulse and momentum were
used. The effect of the moment impulse on the angular velocities was taken into
account through the use of a moment coefficient of restitution.
Kane and Levinson [10, 11] considered the generalized impulse and momentum equations for impact with friction. The impact equations include the generalized speeds before and after the impact. The system of equations was solved with
two assumptions involving the velocity of separation and the normal and tangential
impulse.
The planar body collisions with friction were studied by Wang and Mason [12].
Routh’s graphical method was employed to analyze the frictional impact. Poisson’s
and Newton’s methods were used for the impact analytical expressions. They show
that Poisson’s hypothesis does not violate energy conservation principles, while Newton’s coefficient of restitution is not always correct.
Johansson and Klarbring developed an algorithm for rigid body impact with friction [13]. The impenetrability condition and Coulomb’s law of friction are formulated as equations and solved together with the equations of motion using Newton’s
method. The impact process is described by the coefficient of friction, the coefficient
of restitution, and a new introduced coefficient of tangential restitution. The new
coefficient is determined experimentally.
As it can be noticed from the previous literature, most of the cases involved
impacts with Coulomb friction. In this study, during the impact a friction force based
on Benson model is employed.
2 Mathematical Model
2.1 Kinematics
Figure 1 is a schematic representation of a kinematic chain with two links 1 and 2. The
mass center of the link i is at C i , i = 1, 2. The dimensions are OC 1 = C 1 A = L 1
and AC 2 = C 2 T = L 2 . The “fixed” Newtonian reference frame (0), RF0, has the