Beam-based Nonlinear Spring


When the nonlinear spring is implemented as a load cell, the logarthimically stiffening load cell can be used for weight or force measuring applications that involve large force ranges (up to 5 orders of magnitude). Applications may include robotics, agriculture, and drug delivery. The nonlinear spring can also be used for energy harvesting from ambient vibrations, shock absorption for external loads, and passive control or suppression of mechanical instabilities involving targeted energy transfer from one component of a structure to another.

Problem Addressed

Linear load cells suffer from limited range due to low resolution at low forces or oversensitivity at high forces (causes mechanical failure). This stiffening mechanism allows the load cell to be ultrasensitive at low forces and less sensitive at high forces- so that the signle mechanism can measure forces with a resolution of 1% over 5 orders of magnitude (e.g. from 1 gram [the mass of a cotton ball] up to 100 Kg [the mass of a baby elephant]). In ambient vibration energy harvesting applications, energy harvesting is inefficient because of the uncertain character of the excitation (e.g. someone’s vibration characteristics are very different when walking or running). This is overcome by using a nonlinear oscillator system, which induces adaptability to the different signals to maintain good power performance


The nonlinear spring consists of a flexible cantilever or ring that increasingly wraps around a carefully designed rigid surface as increasing force is applied. As the flexible elements wraps along the rigid surface, its effective length shortens, which causes the structure to effectively stiffen. This design has minimal frictional losses and moving partsFor the load cell application, two designs were experimentally verified to allow 1% measurement resolution over 0.01-1,000N of applied force. For the energy harvesting application, a nonlinear energy harvester was optimized and numerically simulated for power robustness for walking, walking quickly, and running. The nonlinear systemnearly doubled the average harvested power compared to linear harvesters.


  • Force or weight measurement over large ranges (up to 5 orders of magnitude)
  • High power conversion efficiency over different excitation signals
  • Ability to harvest vibrational energy