Dynamics and energy efficiency of jumping systems

Abstract

Previous mechanical design guidelines for jumping robots focus on performance optimisation for a specific task, such as jumping to a given height above the ground. In doing so, numerous designs have been proposed with different drivetrains and structures, from the prismatic motor-driven monopod to the recent nonlinear spring-driven linkage. An intuitive approach to increasing the jump height is to use a more powerful drivetrain, however this would also increase the system weight and impact the attainable jump height. Previous research has not fully addressed this trade-off, and how it varies with system scale. This poses a design challenge in selecting the appropriate drivetrain and overall system scale to achieve a target jump height. This thesis develops a dimensionless dynamic framework to obtain the theoretical upper bound of the jump height of jumping drivetrains across different scales and gravitational conditions. The analysis shows that an ideal spring-driven system charged by a motor jumps higher than the equivalent motor-driven systems for all scales. To reach the theoretical maximum jump height at a given system scale, the system must maximise the elastic energy stored in a spring, and fully convert the stored elastic energy into kinetic energy at take-off. An energetics analysis of spring linkages shows that the elastic energy stored in a spring is maximised by using a constant force spring. These can be practically realised by combining simple rotational linkages with linear springs. However, for the acceleration phase of the jump a spring-driven rotational linkage is shown to take off before the elastic energy is converted to kinetic energy due to centripetal forces acting on the links. Simpler spring-driven prismatic systems avoid this problem, but have limited elastic-kinetic energy conversion due to momentum transfer to the unsprung foot mass. The models demonstrate for springlinkage system design there is a trade-off between efficient storage of energy, and efficient release of energy. The findings provide practical guidance for improving the overall energy conversion efficiency for future jumping robotic systems.

Date of Award	31 Oct 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	william crowther (Supervisor) & Ben Parslew (Supervisor)