Belt Drive Center Distance (for a Standard Belt)

Belts come in standard lengths, so once you pick sheaves and a belt off the shelf you solve for the spacing to set the motor slide base. From L = 2C + (pi/2)(D+d) + (D-d)^2/(4C), with A = L - (pi/2)(D+d), the center distance is C = [A + sqrt(A^2 - 2(D-d)^2)]/4. Also reports the wrap angle on the small sheave, 180 - 2 asin((D-d)/2C), because a V-belt's HP rating is tabulated at 180 degrees and derates below it (about 20% down at 120 degrees). A 10 in and 4 in sheave pair on a 62.44 in belt sets a 20.0 in center distance with 162.8 degrees of wrap. Use pitch diameters and the belt pitch length; a real drive still needs take-up (move in to install, out to tension and follow stretch). A design aid; the manufacturer's tables govern.

A = L - (pi/2)(D+d); C = [A + sqrt(A^2 - 2(D-d)^2)]/4 (inverse of L = 2C + (pi/2)(D+d) + (D-d)^2/(4C)); wrap on small sheave = 180 - 2 asin((D-d)/2C) deg.

The center distance for a standard belt - the inverse of the ANSI/RMA IP-20 / IP-22 belt-length equation, as in the Gates Industrial Drive Design Manual (public).

Standard drive geometry; the sheave pitch diameters and the belt pitch length come from the user. Free at gates.com/literature.

Estimate. AHJ and licensed mechanical contractor govern. ACCA Manual J / D / S supersede rules of thumb.

Field names used by the API: large_pitch_diameter_in, small_pitch_diameter_in, belt_pitch_length_in, center_distance_in, wrap_small_deg

• Center distance C = [A + sqrt(A^2 - 2(D-d)^2)]/4, the larger (+) root of the belt-length quadraticinverse of ANSI/RMA IP-20 / IP-22
• Wrap angle small-sheave wrap 180 - 2 asin((D-d)/2C); below 180 deg the V-belt HP rating deratesGates Industrial Drive Design Manual
• Scope nominal center distance; RMA/ISO take-up (install slack and tension/stretch allowance) is separatescope of this tile