Flexure Coupling Mechanisms for High Performance Robotics and Automated Processes

Student thesis: Doctoral ThesisPhD


Flexure couplings are used in machines and systems because they have simple structures and can eliminate many negative effects occurring in other traditional joints, such as ball bearings and hinges. However, the behaviour of flexure coupling is difficult to predict due to its non-linearity. In this thesis four different compound flexure couplings have been investigated, which are a two-section parallel-link flexure coupling, two-section cross-link flexure coupling, triple-section cross-link flexure coupling with flat middle strip and another with deformed middle strip. Initially, a set of first-order differential equations based on large deformation Euler-Bernoulli theory with corresponding boundary conditions modelling a single-section plain flexure coupling is validated. The model is then expanded to predict the deformations of the four compound flexure couplings, by combining with a multi-step optimisation scheme. Corresponding validation experiments are designed to measure the deformed shape of the flexure couplings constructed from spring steel section and aluminium blocks. The predictions obtained match the deflected shape well.

An experimental rig, comprised of three rigid bodies which are linked by the flexure coupling is examined, where linear actuators are used to deflect flexure coupling through an actuator mechanism. For the multi-body system, each actuator mechanism is investigated when a multi-section flexure coupling making the system completely bearing free. The method utilising the multi-step optimisation scheme requires a sufficiently accurate initial estimate for forces imposed at the end of flexure couplings and deformed angle, however it is impractical to derive the required parameters. Therefore, this method has limited capability in this case. Instead, a co-rotational beam method is introduced to predict the movement of the multi-body system. Due to the limited movement of the two-section parallel flexure coupling, it was not tested in the multibody system. Two experiments were performed to validate the mathematical representation. Initially a single-section flexure coupling based joint is examined where the solver prediction of the behaviour is tested against the experimental rig. The theoretical results matched the experimental data well. Therefore, the full multibody system comprising of the flexure coupling joints is investigated in the next step. The modified solver was adapted to predict the movement of the whole experimental rig. The predictions have a small difference where compared to the experimental results, however it can be considered as a reliable method.

In the final part of the thesis, trajectory control is investigated. A multi-step optimisation scheme is adapted to find the necessary actuator extensions so that the experimental rig can move along a given demand trajectory. Applying a correction on the control, identified through experimental testing, trajectory tracking to within around 2 mm can be achieved.
Date of Award18 Jan 2023
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorNicola Bailey (Supervisor) & Patrick Keogh (Supervisor)

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