1.       Figure P12-2 shows an involute of a circle that starts at point (0, rb) and continues to point P (x, y). The angle θ is known as the roll angle and φ is the involute pressure angle. Derive expressions for the and coordinates of in terms of the base circle radius rb and the involute pressure angle only. Plot vs. over the range 0° < φ=””>< 40°=”” for=””>rb = 2 in.

2.       A 39-tooth spur gear is in mesh with an 18-tooth pinion. The pd = 8 and φ = 25°. Find the contact ratio

3.       A 79-tooth spur gear is in mesh with a 20-tooth pinion. The pd = 8 and φ = 20°. Find the contact ratio.

4.       What will the pressure angle be if the center distance of the spur gearset in Problem 12-39 is increased by 6%?