Solving a Construction with 3 Degrees of Freedom

[azizz]

Hey,
For a school project we have a construction as indicated in the attached figure.

The idea is that point A is able to move in 3 degrees of freedom, but the position, velocity and acceleration of this point is known. The length ||A-P1|| is fixed and is connected to a bell crank that is able to rotate about the y-axis only (with the center of rotation located in C). The length between P2 and B can change (its an actuator). Point B is fixed.

Now I'd like to compute the velocity of the actuator given the velocity of point A.

I have difficulties to setup the correct equation. Mainly because I don't know how to obtain a correct equation of, for example, the angle of the bell crank. Can someone help me with a initial setup of the equations?

Thx in advance.

 

[Navin A S]

To solve this problem, you need to use the velocity transformation equations. These equations are useful for determining the velocities of points and objects in different frames of reference. In your case, you need to determine the velocity of the actuator relative to the frame of reference of point A. First, you need to define your coordinate system with respect to point A. Let's assume that the x-axis is along the line AP1, the y-axis is perpendicular to AP1 and the z-axis is perpendicular to the xy-plane. Now, you need to derive the equations of motion for the position and orientation of the bell crank. Let's denote the position vector of point P2 with respect to point A as rPA and the orientation of the bell crank with respect to the xy-plane as θ. The position and orientation of the bell crank can be expressed as: rPA = ||AP1|| + ||P2-B||cosθ θ = arcsin((P2-B)/(||AP1||+||P2-B||)) Using these equations, you can then derive the velocity of the actuator relative to point A. The velocity of the actuator with respect to point A can be expressed as: Vactuator = vA + ωAB x (||AP1||+||P2-B||cosθ) where vA is the velocity of point A and ωAB is the angular velocity of the bell crank with respect to point A. Hope this helps!