Kinematics of Delta-type Parallel Robot Mechanisms via Screw Theory: A tutorial paper

In the past decade, parallel manipulators began gaining more attention since they can outperform their serial counterparts at several areas. The use of common parallel delta robot mechanisms is wide-spread within the industry, especially for fast pick and place applications. There is a new type of parallel mechanism on the rise, called the Generalized Triangle Parallel Robot (GTPR), where the parameters of the robot may differ from arm to arm. Due to the asymmetric structure, the kinematic description of such a mechanism is less trivial. For this reason, we wish to show that many mechanical problems become more straightforward by using screw theory througout the formalism. Screw theory uses the Plücker coordinate representation of mechanical structures. This representation leads to an elegant and tractable form of the kinematics equations. This paper presents a compact tutorial about screw theory and a joint velocity calculation example, with the complete derivation of screws and numerical results.