A planar parallel 3-RRR robot with synchronously driven cranks

• F-mechanisms which have three synchronously driven cranks are introduced.
• A complete analysis and synthesis of the mechanism is examined.
• The result for complete turnable of mechanism is given.

This paper focuses on the analysis and synthesis of F-mechanisms, i.e., of planar parallel 3-RRR robots with three synchronously driven cranks. These are high-speed planar mechanisms, which allow modifying the periodical constrained motion by phase shifting during operation. There is a broad variety of obtainable constrained motions — including a permanent stillstand.The velocity analysis reveals that there are poses with either no pole configuration or an infinite number of pole configurations. These singular resp. twofold singular poses can be geometrically characterized. It turns out that in general the singular poses are those where the cranks need to reverse the rotation in order to perform the full motion. At twofold singular poses bifurcations can take place. The constrained motions are algebraic of degree 6. The question of whether the active bars of a given F-mechanism are completely turnable can only be cleared from case to case by a numerical analysis. Here a particular diagram which indicates reverse poses as well as bifurcations is useful.