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

Spring force vs. angle:

Reaction force vs. angle:

Spring constant with varying angle:

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

Spring constants in different units:

We have found spring constants of 750 lbf/in, so this concept seems to be workable.

We haven't dealt with friction here, though. That may make a difference in our final results.

Concept 2

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

(1) the force acting on the ball from the applied torque, Ftorque

(2) the spring force, Fspring

The these forces can each be broken down into two components. The one we are going to deal with is the reaction force acting on the ball from the hole, Frxn

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 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:

The reaction force from the torque acting on the ball can also be found:

Then the spring force is determined as follows: