Engineering
Increase the output load until the drive stalls. Change the tooth ratio and reverse the motor.
Rigid shafts and an ideal gear constraint. Tooth contact, backlash and elastic deformation are not resolved. Motor and load torque are finite.
Equations ω₁ + (z₂/z₁)ω₂ = 0; J Δv = impulse
Engineering
Change the helix angle and hand at the same load and read the axial thrust on the bearings. The tooth force is solved along the tooth normal; the thrust is a bearing reaction, not a formula.
Engineering
Turn the shafts to another angle and change the tooth ratio under the same load. The pitch cones follow; input and output power stay equal in the ideal mesh while torque and speed trade places.
Engineering
Lift a load through a worm and wheel, then stop the motor and lower the friction until the load turns the worm back. Compare one, two and four starts: the efficiency both ways and the brake needed to hold the load.