I have some question to ask for calculation of the tension force that supplied from a rotating motor (which is shown in the attached image).
I would like to calculate how much is the force created to pull the tension downward and the distance moved linearly downward. These calculation is related to the angle that motor rotated.

Could someone gives me idea/principle on calculating these forces.

To calculate the force which the string being pulled down upon can see, look up the stall torque of the motor you’re using. This should be in Nm, in*Lbs, or some other distance times a force, so when you divide the torque (lets say in Nm) by the length of the arm you’re using (lets say in meters) you get the force exerted by the motor (in this case in newtons).

The force downward is related to the angle the arm of the motor makes with the vertical by a sin function.

How far the string gets pulled downward depends on what it’s connected to, but if it’s just connected to a fixed object, the distance it gets pulled downward will involve the spring constant of the string and it’s length. Basically, you’re going to want to find the distance the string gets pulled where the force of the motor (equal to sin(theta)*torque/arm length) equals the spring constant K times the length the string has been pulled. Keep in mind that theta and the distance the string has been pulled are related, and solve algebraically.

What does the dashed circle in the attached diagram represent? It seems to be labeled “Path of rotation,” but I can’t tell which object would follow this path, especially since there does not appear to be a point of rotation at the center of this circle.

all right, thanks a lot. One more question to ask, if the tension is connected at the end of a bendable rod. Can I calculate the what angle will it bend as the motor turn?

the dashed line is the rotation path of the arm. When it rotate and connect with the ring(small circle), the ring move along the path as well.

Where is the point around which the system rotates? Is it at the center of the smaller circle that has arrows around it? Or is it at the joint between this circle and the arm of length l.