Diagram shows a shaft A B C containing two gears at B and C which is connected to a motor A where the torques of 20 Newton meter and T subscript c is applied on B and C and the distance A B is 1400 millimeter and B C is 1000 millimeter. The x axis is taken along the axis of the gears and the y axis is taken along the motor support at A and perpendicular to the x axis.

Substitute the torque-twist relationships:

ϕ1=T1L1J1G1   and   ϕ2=T2L2J2G2

into the geometry of deformations equation:

ϕC=ϕ1+ϕ2

to derive an equation for the rotation angle at C:

ϕC=T1L1J1G1+T2L2J2G2