[Paper Review] Elastic energy storage of spring-driven jumping robots

J.T. Lo, Ben Parslew|arXiv (Cornell University)|Nov 3, 2023

Robotic Locomotion and Control4 citations

TL;DR

This paper presents a generalized energetics analysis of rhomboidal linkage-spring systems in spring-driven jumping robots, demonstrating that combining horizontal translational springs at the diagonals of a rhomboidal linkage creates a near-ideal constant-force spring that stores up to 160% more elastic energy than prior designs, significantly increasing jump height for a given motor force.

ABSTRACT

Spring-driven jumping robots use an energised spring for propulsion, while the onboard motor only serves as a spring-charging source. A common mechanism in designing these robots is the rhomboidal linkage, which has been combined with linear springs (spring-linkage) to create a nonlinear spring, thereby increasing elastic energy storage and jump height for a given motor force. The effectiveness of this spring-linkage has been examined for individual designs, but a generalised design theory of this class of system remains absent. This paper presents an energetics analysis of the spring-linkage and provides insight into designing an ideal constant force spring, which stores the maximum energy for a given motor force. A quasi-static analysis shows that the force-displacement relationship of the spring-linkage changes with the orientation and type of the spring, but is independent of the linkage scale. Combining different types and orientations of springs within the linkage enables higher elastic energy storage than using single springs. Placing two translational springs at the diagonals of the rhomboidal linkage creates an ideal spring that could increase the jump height of prior robots by 50-160%.

Motivation & Objective

• To address the limited elastic energy storage in spring-driven jumping robots due to motor power and velocity constraints.
• To develop a generalized design theory for spring-linkage mechanisms that maximize mechanical-elastic energy conversion efficiency.
• To identify optimal spring types, orientations, and placements within rhomboidal linkages to approach ideal constant-force spring behavior.
• To quantify the energy storage potential of hybrid spring-linkage configurations compared to linear and ideal springs.
• To enable higher jump heights by decoupling jump performance from motor limitations through enhanced elastic energy storage.

Proposed method

• Conducting a quasi-static force-displacement analysis of rhomboidal linkages with various spring types and orientations.
• Modeling the spring-linkage system as a nonlinear spring with variable stiffness based on linkage geometry and spring placement.
• Using normalized force and displacement to compare energy storage across different spring-linkage configurations and ideal/linear spring models.
• Deriving theoretical elastic energy storage using the formula EPE = ∫F dx, with F representing the spring force and x the displacement.
• Evaluating the performance of hybrid configurations combining translational and rotational springs in rhomboidal linkages.
• Assessing the impact of spring stiffness, orientation, and linkage scale on energy storage efficiency, independent of system size.

Experimental results

Research questions

• RQ1 How does the force-displacement relationship of a spring-linkage system vary with spring type and orientation within a rhomboidal linkage?
• RQ2 What spring-linkage configuration maximizes elastic energy storage for a given motor force, approaching the theoretical limit of an ideal constant-force spring?
• RQ3 Can combining different spring types (e.g., translational and rotational) in a rhomboidal linkage yield higher energy storage than single-spring arrangements?
• RQ4 How does the energy storage of real spring-linkage systems compare to ideal and linear spring models under identical force-to-weight ratios?
• RQ5 What are the practical trade-offs in spring stiffness and exposure when optimizing for compactness and environmental protection?

Key findings

• Placing two translational springs at the diagonals of a rhomboidal linkage creates a near-ideal constant-force spring, increasing elastic energy storage by up to 160% compared to prior spring-driven jumping robots.
• This diagonal spring arrangement stores approximately 100% of the energy of an ideal spring, achieving near-perfect mechanical-elastic energy conversion efficiency.
• A configuration using rotational and horizontal springs stores up to 97% of the energy of an ideal spring, offering a high-performance alternative with better mass distribution.
• The rhomboidal linkage with springs nearly parallel to a link stores around 65% of the ideal spring's energy, providing a compact and protected design at the cost of increased stiffness requirements.
• Rotational springs at any joint offer design flexibility for mass distribution, which is critical for efficient elastic-to-kinetic energy conversion.
• The energy storage performance is independent of linkage scale, enabling scalable design across different robot sizes.