17,18 Unfortunately, the constant force mechanism indicates a zero-stiffness and low resonant frequency. 15,16 For these kinds of constant force mechanisms, the position control and force control are not required, which provides a good way to generate the constant force. A vibration isolation system using the negative stiffness is designed to obtain a lower frequency. The positive stiffness can be generated by the deformation of leaf beams, while the negative stiffness is proposed based on the buckling of prestressed bars. Thus, a constant force output is realized by the developed structure. The constant force mechanism does not obey Hooke’s law and can realize a zero stiffness with a large displacement output, which is realized by combining a positive-stiffness mechanism and a negative-stiffness mechanism together to obtain a zero-stiffness mechanism. 14 Unlike the traditional elastic mechanism, a new kind of constant force mechanism has been developed. Recently, several zero stiffness flexure mechanisms have been proposed to obtain the constant force. Thus, the force sensor-based feedback control system needs a complicated algorithm implementation to obtain a constant contact force environment. 13 Although the force information on the mechanism is available, the contact force between components is difficult to control accurately. Because the force sensor is sensitive to the relative displacement, it is difficult to control the displacement accurately. 12 It is more complicated to utilize the feedback control algorithm to improve the accuracy of the constant force. To realize high precision, the whole structure parameters should be analyzed to guarantee the limited value for deformation within the elastic domain. 10,11 In addition, for the compliant mechanism, the main deformation usually occurs at the flexible hinges. 8,9 Furthermore, in order to overcome the nonlinearity of the implicit model, the precision position control and feedback control methods are necessary for the compliant mechanism. The control techniques include the force/position switching control and impedance control. However, it needs to design the real time and complex algorithm to control the force and displacement simultaneously. The constant force is usually realized by the feedback control methodology with precision force sensors and controllers. Experimental results demonstrate that the developed constant force mechanism has a constant force with slight fluctuation with a range of 500 μm. It is noted that the constant force mechanism can be robustly controlled by a proportional-integral-derivative control method. The open-loop and the closed-loop experimental tests are implemented to investigate the performance of the developed constant force mechanism. Finally, a prototype is fabricated using 3D printing technique. Additionally, the parametric model of the proposed mechanism is investigated using the nonlinear finite element analysis. Based on the established model, the performance of the constant force mechanism is evaluated computationally. Furthermore, the elliptic integral method and the pseudo-rigid-body approach are utilized to establish the model of the constant force mechanism. The regular structural holes can reduce the mass and stiffness of the whole mechanism. Meanwhile, the positive stiffness is generated by the leaf flexure hinges with structural holes. In order to achieve a low driving force, the negative stiffness is realized by a special bistable beam, which is a step beam with structural holes. The constant force is generated by using the combination of a negative-stiffness and a positive-stiffness mechanism. Unlike the conventional force control method using a force sensor and feedback controller to obtain constant force output, the proposed compliant mechanism provides a constant force utilizing the unique mechanical property of the mechanical structure. This paper presents a novel design of a flexure-based constant force mechanism with a long travel stroke.
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