Elastic joints: the secret to smarter, adaptable robots

Today's robots need to move smoothly, adapting to changes in their surroundings. Researchers have studied a special mechanism that uses elastic joints to vary the force a motor can apply. Imagine a mechanical arm that, when it meets a heavier obstacle, can soften the impact instead of stopping. This is possible thanks to elastic elements that compress and expand, distributing energy intelligently. The team used mathematical equations and computer simulations to understand the system's behaviour. They found that, with constant input power, the output speed self‑regulates: the heavier the load, the lower the speed, and vice‑versa. This automatic adaptation helps the robot save energy and reduces component wear. Tests showed the system can handle variable loads without losing precision, a key advantage for industrial production lines and collaborative robots working closely with people. In industry, loads change constantly: a robot picking items of different shapes must adjust the gripper force to avoid breakage. Elastic joints create a 'force memory', allowing the robot to sense resistance and adapt in real time. This not only improves work quality but also cuts energy use, essential for sustainable factories. The researchers also demonstrated integration with adaptive vibration actuators, which use quick micro‑movements to correct positioning errors. Combining elasticity with smart control opens new possibilities for collaborative robots, drones and autonomous vehicles, where safe interaction with the environment is critical.

The dynamic modelling of the two‑degree‑of‑freedom system uses generalised coordinates q = [q1, q2]ᵀ, where q1 describes the motion of the moving body and q2 the deflection of the elastic joint. The Lagrangian formulation yields the equations of motion:

M(q) q̈ + C(q, q̇) q̇ + K(q) q = τ + F_ext,

with the mass matrix M, the Coriolis/Centrifugal vector C, the stiffness matrix K, the input torque τ and the external force vector F_ext. For the linear case, M, C and K are constant, allowing an analytical modal analysis. The eigen‑modes reveal coupling between the rigid‑body rotation mode and the flexible joint mode, with natural frequencies f1 ≈ 12 Hz and f2 ≈ 45 Hz. The adaptive vibration actuator adds a speed‑proportional control term, τ_ctrl = -k_p·(q̇ - ω_ref). Numerical integration (4th‑order Runge‑Kutta) shows total kinetic energy oscillating within 5 % over load cycles, indicating efficient internal energy redistribution. Force adaptation appears as F_out = k·δ, where δ is the joint deformation. With constant input power P_in, the output speed follows ω_out = P_in / (F_out·r), confirming the inverse load‑speed relationship. Energy‑efficiency analysis quantifies an 18 % reduction in mechanical losses compared to a rigid‑joint counterpart, thanks to the integrated viscous damping (c = 0.3 Ns/m) in the joints. Experimental validation on a robotic test bench confirms the model’s robustness for automation and collaborative‑robot applications.