How to Calculate Pitch Diameter, Angle and distance between two Spheres! I'm trying to figure out how to calculate the Angle [A], Pitch Diameter[P], and Circumferential Clearance depending on how many spheres are in the complement and inner diameter[S]  and outer diameter[B]. According to the following diagram.

 A: Let $n$ be the number of bearings (circles). Then,
$$A = \frac{360°}{n}$$

Pitch radius is inner radius plus radial clearance plus bearing radius. Using diameters, we need to count the clearance twice:
$$P = S + 2 D + N$$
On the other hand, outer radius is pitch radius plus bearing radius. With diameters, that means
$$B = P + N = S + 2 D + 2 N$$
If we know inner and outer diameter, as well as bearing diameter, then we can solve the radial clearance $D$ from above; it is
$$D = \frac{B - S}{2} - N$$

Circumferential clearance $C$ is a bit tricky, because you have marked it along the dotted circle. If you calculate it that way, you get an overestimate -- as in, you cannot fit a piece of that thickness between the bearings. Consult this diagram instead:

Here, $r = N/2$ and $R = P/2 = (S+N)/2 + D$.
The diagram forms two equal right triangles on top of each other, mirrored vertically, so
$$\sin\frac{A}{2} = \frac{r + C/2}{R}$$
Solving for $C$, and substituting the original variables, we get
$$C = \left(S + N + 2 D\right)\sin\left(\frac{A}{2}\right) - N = \left(S + N + 2 D\right)\sin\left(\frac{180°}{n}\right) - N$$
