Direct Kinematics for All Planar Three-Legged Parallel Platforms: Kinematic Mapping

Kinematic mapping is a valuable tool to deal with difficult direct kinematics problems. It should have successful application in other areas of kinematics as well. However, it has been ignored by most engineers. One reason may be that it is rooted in 19th century projective geometry, while most engineers are familiar only with the older, traditional Euclidean geometry. Hence, many reject kinematic mapping at the first glance when confronted by its peculiar, sometimes intuitively unrealistic, possibly confusing and overly complicated concepts. It is humbly suggested that we might initially avoid the details of the basic geometry in order not to scare off potential users when introducing them to kinematic mapping. The authors found this tool to be easy to use but difficult to understand. Therefore, it may obtain wider acceptance if we focus first on actual applications before becoming enmeshed deeply in the theoretical background.