Abstract: An indexing apparatus (10) is disclosed which is designed for use with various types of work transfer equipment and is operative to provide smooth rapid jerk-free acceleration and deceleration whereby workpieces may be smoothly and rapidly transferred between operating stations. The indexing apparatus (10) includes suitably arranged cams (90, 90', 106, 124, 130, 132, 150, 162, 180) and cam followers (38, 52, 114, 116, 166, 168, 174) which operate to convert a driving input motion which is typically rotary in nature to a desired output motion which may be either linear or rotary but which is characterized by substantially jerk-free, smooth acceleration and deceleration at the beginning and end of the respective indexing movements. In one embodiment the apparatus comprises a crank arm (22) having cam followers (38, 52) provided thereon which control pivotal movement of transfer arm (58) which is in turn connected to a linearly reciprocable apparatus which may include a work supporting surface for example.