Tables of calculated values for spring constant and vertical force with varying theta:

Spring constant with varying angle:

Vertical force vs. angle of reaction force:

This force, together with the distance moved, determine the spring constant k:

The vertical force acting on the ball can also be found:

Concept 2

There are three forces to be considered here in a summation of forces:

(1) the force acting on the ball from the other plate, F

(2) the spring force, Fspring

(3) the frictional force, Ffriction

The force acting on the ball, F, can be broken down into two components. These are:

(1) the force from torsion, FT

(2) the vertical force, Fy

The diameter of the part is 18mm. Therefore, the distance of the ball from the center of the part, rposn can be approximated. The radius of the ball, rb, must also be known.

The size of the ball determines the distance moved by the piston as follows:

The applied torque, T, at disengagement is given. (T = 30 in-lbs).

The angle at which F acts on the ball can be specified. The optimal angle, q , will be the one which allows for the smallest spring constant k.

The force acting on the ball due to the applied torque can be found from the position of the ball as follows: