Mechanical synthesis for nonlinear passive

1. Nonlinear passive stiffness using mechanical singularity

For the realization of nonlinear passive stiffness, a nonlinearity of material is sometimes utilized. For example, SMA (Shape Memory Alloy) has super elasticity which realizes low stiffness. In this research, nonlinear passive stiffness is realized by a linear spring and nonlinearity of mechanism. The following figures show the designed mechanism.
The stiffness profile of this mechanism is shown in the following figure. The stiffness is zero when the rotational angle equals to zero, which is realized by mechanical singularity. According to the larger rotational angle, the stiffness changes to the higher.
A four legged robot is designed using the proposed mechanism in the knee joint.

2. Mechanical synthesis for nonlinear passive stiffness

In this research, a variable stiffness is realized by "robot motion" + "nonlinear stiffness". For this purpose, an arbitrary profile of nonlinear stiffness has to be synthesized. The following mechanism is designed and link parameters are optimized so that the reaction force realizes the given profile as shown in the right figure to absorb the impact in landing.
By the optimization procedure, the configuration of the mechanism is obtained as shown in the following left figure, and the reaction force is realized as shown in the right figure.
Moreover, using the optimized parameters, a prototype is designed and reaction force is measured as shown in the following figures. We can see that the desired profile is realized.
The following movie shows an experimental result.

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