The use of surface generation in the design and analysis of linkages with different types of singularities in the configuration space

Student thesis: Doctoral ThesisDoctor of Philosophy


In mechanisms theory it is often desired to come up with techniques that allow reducing a complex mechanical problem to a simpler mathematical task. The use of surfaces generated by kinematic chains in the analysis and design of linkages reduces the problem to the analysis of surfaces in three dimensional space. Hence, the rich knowledge on surfaces and their intersections becomes a powerful tool to solve the problem.

Surfaces generated by kinematic chains were used to aid the design of linkages since as early as the 70s. However, after a few publications, several of which remained rather obscure conference papers, the technique was abandoned. More recently, the analysis of the intersection of surfaces was applied in the design of reconfigurable mechanisms, a topic still not of the interest of researchers when generated surfaces were explored first. This recent application opened the doors to the question whether the use of surfaces could help the design and analysis of linkages for other purposes and unsolved problems in the research field.

Therefore, in this thesis, surfaces generated by kinematic chains are further explored to bring fresh results including kinematotropic linkages, paradoxical reconfigurable linkages, reconfigurable parallel manipulators that can change their number of degrees of freedom between three different values, and spatial linkages with a cusp in their configuration space. Furthermore, the use of generated surfaces will prove the existence of other types of singularities which had not being explored before, namely the intersection of cusp and curves, and the intersection of cusp and surfaces. Similarly, in this thesis, a method for designing linkages with a tangential intersection in the configuration space is presented for the first time.

In this thesis, the use of generated surfaces is combined with other techniques including group theory and screw theory, while local analysis is carried out by computation of the kinematic tangent cone at the analysed configuration. The results presented in this thesis prove the reduction to generated surfaces is an effective tool in research in mechanisms theory.
Date of Award1 Jan 2021
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorJian Dai (Supervisor)

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