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Figure P12-2 shows an involute of a circle that starts at point A (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 x and y coordinates of P in terms of the base circle radius rb and the involute pressure angle only. Plot y vs. x over the range 0° < φ=””>< 40°=”” for=””>rb = 2 in.

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

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

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

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