Belts
Tension ratio
and
T1 = Tension in the tight side, T2 = Tension in the slack side,
θ = Angle of contact in radians;  = coefficient of friction
Maximum allowable stress  = Tmax /A
Maximum Tension
Tmax = T1 + T2
Maximum power transmitted: P = (T1 – T2) v
Centrifugal tension
Tc = m v2
For Maximum power:
Tc = Tmax / 3
m: mass, v: velocity
and
T1 = Tmax − Tc
Velocity of the belt at maximum power
V-Belts
Tension ratio:
2= Angle of the groove
Length of belt for an open belt drive,
Angle of lab:
𝑟1 − 𝑟2
𝑥
sin 𝛼 =
Chains
The pitch of the chain:
Radii of the large and small sprockets:
m=x/p
x = centre distance, p = pitch of the chain.
length of the chain
Speed ratio between driver and driven
N1, N2 are angular velocities, d1, d2 diameter,
T1, T2 number of teeth
Also
Brakes
Braking torque:
TB = Ft r
Ft = frictional force on the contact surface.
 = Angle of lap (or embrace)
when  > 60o the equivalent coefficient of friction
Band brakes
Braking torque on the drum: TB = (T1 – T2) re
Effective radius of the drum: re = r + t/2
t = band thickness
Band and block, number of blocks (n):
Dynamometers
Prony dynamometer:
Breaking power
W = Deadload; S = Spring balance, D = Diameter of the wheel, d = diameter of rope,
N = Speed of the engine shaft in r.p.m.
Gears
Module:
m = D /T
Circular pitch: pc = π D/T
D : diameter ; T: number of teeth
D1 and D2 : pitch circle diameters
T1 and T2 : number of teeth
Balancing
Horizontal components:
H = m1r1 cos1 + m2 r2 cos2 + ...........
Vertical components:
V = m1r1 sin1 + m2 r2 sin2 + ...........
Resultant centrifugal force R:
R = √(H)2 + (V)2at
tan‘ = V/ H
Balancing force FC = R
FC = m r
where m = Balancing mass, and r = radius of rotation.