# Normal of two tangent circles

1. Jul 17, 2012

### gogogsr

Hey guys,

i'm building an apparatus with a sliding pin containing a spring and a ball. I want to lock in two different positions so i've rounded two slots in the housings. I would like to know what is the equation two find the normal force of the spring on the ball depending on the displacement of the pin. I'm having a hard time finding the normal with an equation, i can find it manually by moving the pin at different points and then drawing the tangent and normal to find the angle but i know there must be an equation. the slot diameter is bigger than the ball diameter to make sure it slides easily (meaning the slot and ball are not concentric)Thanks guys

2. Jul 17, 2012

### Staff: Mentor

Shouldn't the normal force of the spring on the ball just be k * Δx?

3. Jul 17, 2012

### gogogsr

yes but i want it in the movement direction of the pin so perpendicular, in relation with the ball normal angle on the slot

4. Jul 17, 2012

### Staff: Mentor

Are you trying to calculate the force required to move the pin when the ball is in one of the slots? And that's why you are looking for a normal force, so you can use F = μ * N ?

5. Jul 17, 2012

### Studiot

I would recommend you slightly round the land between the detent poitions to ease tha passage of the ball.
That will happen anyway with wear, but the mechanism will then become sloppy.

6. Jul 18, 2012

### gogogsr

yes, that is exactly what i'm looking for, but with the use of an equation to get the normal angle vs stroke of ball.

thank you

7. Jul 18, 2012

### gogogsr

yes i know i'm putting small radius on the land, thx

8. Jul 18, 2012

### tygerdawg

I believe the max force would occur at the extreme point of the detent feature. This would happen when sliding starts, and decrease abruptly after that. It's a sine function, isn't it? Resolve that angular force with trigonometry into a force vector parallel with the axis of the hole. But you'll need to amp it up a bit to accommodate non-spericity of the detent, ball/hole tolerance fits & associated friction, etc. UNLESS your detent feature is a cone shape from a drill, then a lot of things change.

Seems you could just use standard ball spring plungers and change as required if it doesn't hold your load. Companies that sell those sometimes have design guidelines that answer many of your questions. But that's just me, being lazy.