1. Tooth dimension accuracy can be measured with the David Brown tangent comparator, shown in (a), which is a special caliper measuring the length of common normals, simply illustrated in (b). Prove, the lengths of the common normals between any two opposite involutes are equal, or LM = LM2 (You may mark the points at which the normals are tangent to the base circle as k and k.) DIMENSION W SET TO GAUGE BLOCKS LIMITED MOVEMENT MICROMETER +50--5 MOVING ANVIL FIXED ANVIL LOCKING RING SETTING TUBES TO GIVE APPROXIMATE DIMENSION W TANGENT TO BASE CIRCLE BASE CIRCLE David Brown base tangent comparator (a) Tooth accuracy measurement (Courtesy of Imgur) M L M2 L k1 k2 m (b) Common normals