A new insight into the coupler curves of the RCCC four-bar linkage

Conference Article


International Workshop on Computational Kinematics (CK)





Doc link


Download the digital copy of the doc pdf document


Based on the condition for four points to lie on the unit sphere, derived using Distance Geometry, a new mathematical formulation for the coupler curves of the RCCC linkage is presented. The relevance of this formulation is not only its simplicity, but the elegant way in which we can obtain the derivative of any variable with respect to any other, and the simple way in which intervals of monotonicity can be detected. All these results are compactly expressed in terms of Gramians and, as a consequence, they have a direct geometric meaning contrarily to what happens with previous approaches based on kinematic loop equations


robot kinematics.

Author keywords

Coupler curves, Distance geometry, RCCC linkage

Scientific reference

F. Thomas and A. Perez. A new insight into the coupler curves of the RCCC four-bar linkage, 7th International Workshop on Computational Kinematics, 2017, Futuroscope-Poitiers, France, in Computational Kinematics, Vol 50 of Mechanisms and Machine Science, pp. 552-559, 2018, Springer.