Ball Detent Spring System

Make a freebody diagram of the parts involved and solve the force equations.

Ted

So... three parts, the head of the wrench, the detent, and the end of the handle of the wrench

1. there is force being applied to the end of the handle
2. the detent has a spring force pushing along the axis of the wrench towards the head and a torque
3. the head of the wrench has a torque

What am I missing?

I've designed a couple ball detent mechanism. Simple (not the same as easy!) in so far as there aren't any big surprises. Lay out the FBD of the ball contact against the spring and other parts and you'll get your answers with no need for additional "fudge factors".

Pretty much any ball plunger manufacturer offers a picture like this one:

That picture makes sense, thanks for the link.

I'm having trouble trying to figure out how to calculate if the detent is sitting on a radius rather than on a countersink angle.

Calculate as a detent being forced to slide on a straight line incline, a wedge.

Ted

The formula in the link given does not consider the contact frictions between the ball & detent surfaces, the ball & housing bore surfaces, or the ball and spring end coil surfaces. And these frictions can be significant.

The only thing you need to consider with a simple static force analysis of this detent mechanism where the ball bears against a radiused groove surface rather than an angular groove surface, is the variation of the contact pressure angle as the ball rolls over the radiused groove surface.