# Explosive Output to Enhance Jumping Ability: A Variable Reduction Ratio Design Paradigm for Humanoid Robot Knee Joint

## TL;DR

This paper introduces a new knee-joint design for humanoid robots that enhances jumping ability by varying the reduction ratio during movement.

## Contribution

The novel variable-reduction-ratio design couples the joint angle with the reduction ratio to improve explosive power output.

## Key findings

- A single-joint platform achieved a 0.63 m high jump, a 31.9% improvement over fixed-ratio baselines.
- The design enabled a humanoid robot to perform a 1.1 m long jump, a 0.5 m high jump, and a 0.5 m box jump.
- The variable reduction ratio extends the high-power operating window by reducing motor speed and power losses.

## Abstract

Enhancing the explosive power output of the knee joints is critical for improving the agility and obstacle crossing of humanoid robots. However, a mismatch between the knee-to-CoM transmission ratio and jumping demands, together with power-loss–induced motor performance degradation at high speeds, shortens the high-power operating window and limits jump performance. To address this, this paper introduces a variable-reduction-ratio knee-joint paradigm in which the reduction ratio is coupled to the joint angle and decreases during extension. Analysis of motor output and knee kinematics motivates coupling the reduction ratio to the joint angle. A high initial ratio increases the takeoff torque, and a gradual decrease limits motor speed and power losses, extending the high-power window. A linear-actuator-driven guide-rod mechanism realizes this strategy, and parameter optimization guided by explosive jump control is employed to select the design parameters. Experimental validation demonstrates a high jump of 0.63 m on a single-joint platform (a theoretical improvement of 31.9% over the optimal fixed-ratio baseline under the tested conditions). Integrated into a humanoid robot, the proposed design enables a 1.1 m long jump, a 0.5 m high jump, and a 0.5 m box jump.