Concatenation of a Frequency Doubling Mechanism to Achieve Higher Frequency Multiplication

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The range of motion of elastic energy sources is limited by the size of its transmission system. To enhance this range of motion without compromising the size, previous research introduced a frequency doubling mechanism with the intention to concatenate these mechanisms. This study serves to achieve higher numbers of frequency multiplication by concatenating up to three frequency doubling mechanisms. A crucial challenge is to reduce the input force required to operate the compliant design, even in the absence of output load, to ensure the output moves twice the distance of the input. The optimization process involved simulations to achieve a near-perfect Geometrical Advantage (G.A.) of 2 while ensuring the highest possible load capacity to minimize force-induced geometrical variations. The optimized mechanism was then statically balanced with buckled beams to minimize the input force of each frequency doubling mechanism. The buckled beams introduced negative stiffness, adding potential energy to counteract forces, and ultimately reducing the input force to approximately 5.3% of the initial force. Three frequency doubling mechanisms were concatenated and experimentally validated, achieving a frequency multiplication of 8. The real prototype demonstrated successful results, although the input force was not entirely eliminated, the desired frequency multiplication was achieved. These results form the basis for a compliant frequency multiplication mechanism, enhancing the range of motion of elastic strain energy sources through the implementation of a compact transmission system.