# A Nonlinear CFD/Multibody Incremental-Dynamic Model for A Constrained Mechanism
## 3 Results  
The streamlines of the multibody mechanisms in the constrained and unconstrained conditions at different simulation times are illustrated in Figure 3. In the unconstrained condition, there were no constrained forces acting on the mechanisms' joint, and the system was moved only under the aerodynamic forces from the fluid, which applies to the mechanism from right to left. Both bodies 1 and 2 at the beginning of the simulation were placed at the same displacements and angles in respect to each other. The results revealed that the unconstrained mechanisms due to their body weight distributions, which act at their centers, tend to change their alignment into the vertical position. The spatial position of body 2 as the aerodynamic forces act from right to left also influences the position of body 1 in a way that at the simulation time of 0.48 s, body 1 rotates, and consequently brings about a considerable distance between two bodies of 1 and 2. However, when it comes to the constrained mechanisms, the most important point is that two bodies kept their inner distance until the end of the simulation time. Another point is that the role of the spatial location of body 2 here does not become dominant in changing the location of body 1. It implies that in a constrained system, the bodies show more realistic moves under the aerodynamic forces, which is preferable in CFD simulations. The contours of the velocity of the multibody mechanisms in the constrained and unconstrained conditions at different simulation times are illustrated in Figure 4. In the unconstrained condition, since the static pressure is placed in front of body 2 due to its vertical location, its angle is increased by the passage of simulation time, and it led to a conversion of pressure in the front and back sides of the body. Regarding body 1, after changing its spatial condition to horizontal, the same pressure conversions in both the front and back sides of this body occurred. This issue is observable at the simulation times of 0.48 s and 1.14 s between the unconstrained and constrained bodies of 1 and 2. At the simulation time of 0.48 s, in the unconstrained condition, the highest velocities were at the end of bodies 1 and 2, while in the constrained condition, the highest velocities were at the joint of bodies 1 and 2. This implies that in unconstrained mechanisms, the distribution of velocities were dramatically affected by the aerodynamic forces acting on the system, whereas in a constrained system, the joint can well manage the aerodynamic forces following by a realistic drop mode analyses. The aerodynamics forces and torques acted on the center of gravities of bodies 1 and 2 in the \(X\) and \(Y\) directions for both the unconstrained and constrained conditions are presented in Figure 5. Under the aerodynamic forces in the unconstrained condition, at the simulation times of 0.6 s for body 1 and 0.25 s for body 2, the motion of the mechanism was changed. In these simulation times, the bodies were at the minimum velocity values. By changing the directions of the force vectors, the bodies of 1 and 2 relatively deviate to left, which is related to the forces in \(Y\) direction. These forces are always positive with the maximum value of 20 N. Meanwhile, as the gravity force of the bodies is \(-20\) N, the summation of these two forces led to a negative acceleration in \(Y\) direction for the unconstrained mechanism. In the constrained mechanism, in most of the simulation time the forces in \(X\) direction were negative, which is related to the direction of the aerodynamic forces acting on the mechanism. When these forces are being compared to those of unconstrained mechanism, their values are two times bigger, which related to the velocity of the flow here (\(-5\) m/s compared to \(-3\) m/s for the unconstraint mechanism). However, the forces in the \(Y\) direction were not altered (\(-20\) N). The momentums here with the passage of simulation time were altered from positive to negative values, which address the rotation of the bodies.