MecMovies 4.0 : M6.18: Motor-driven Shafts

Diagram shows two shafts marked 1 and 2 of length 36 inches and 96 inches respectively. They are connected by two gears at B which has 24 teeth on the shaft 1 and at C which has 72 teeth on the shaft 2. The shaft 1 is connected to a motor at A. The shaft 2 has a gear at D on which a torque T subscript D is applied.

4. To compute the rotation angle of gear $D$ relative to flange $A$ , the angles of twist must be determined using the torque-twist relationship for each shaft. While only the torque magnitude was needed to calculate the shear stress magnitudes, the proper signs for $T_{1}$ and $T_{2}$ are needed to find the magnitude and sense of the angles of twist and rotation angles.

5. Cut a $FBD$ through shaft $(2)$ and around gear $D$ . Establish the proper sign for $T_{2}$ from the equilibrium considerations of this free body.

6. The torque $T_{1}$ must have the opposite sign from $T_{2}$ because the gears at $B$ and $C$ create a reversal in shaft rotation directions.