1. Bevel Gear Background

Bevel gears are used in a wide variety of applications ranging from differential drives to being the main mechanism in a hand drill. They are used in these mechanisms to change the axis of rotation. The common types of bevel gear are straight, spiral, zerol, and hypoid ¹. In the Wild Wild West mechanism, we utilize straight bevel gears.

Some characteristics of bevel gears are their cone-shape. The cone-shape allows for the apices of the 2 gears to intersect. If this intersection does not occur, there will be a velocity mismatch at the gear interface. In addition, the angle between the shafts can be varied to get different output rotations ². In the case of this mechanism, the angle between the shafts is 90° (gamma). The picture below is from page 500 of Robert L. Norton's Design of Machinery text. 

Figure 1: Shows how the apices of the bevel gears must be intersecting

The analysis I did on the mechanism pertained to the velocity, force, and position. For bevel gears, the velocity ratio between the two gears is given by:

where N_in represents the number of teeth of the pinion and N_out represents the number of teeth of the driven gear. For force analysis, I determined that there are three total forces that act on the pinion and driven gear. They are the tangential, radial, and axial forces. The axial and radial forces make up the x and y components of the separating force, respectively.

References:

1. Types of bevel gears are differentiated by the geometry of the overall design.  (2017, November 13). Retrieved from https://true-gear.com/the-types-of-bevel-gears/blog.html

2. Norton, R. L. (2014). Design of machinery: An introduction to synthesis and analysis of mechanisms and machines. New York: McGraw-Hill.