A compliant guiding mechanism utilizing orthogonally oriented flexures with enhanced stiffness in degrees-of-constraint

https://doi.org/10.1016/j.mechmachtheory.2021.104555Get rights and content

Highlights

  • A guiding mechanism is designed to enhance the stiffness along the DOC.

  • The nonlinearity of the guiding mechanism is modeled for large-stroke applications.

  • The model improves the kinetostatic accuracy of a beam with fillets effectively.

  • Simultaneous optimal design of topology and size is proposed for the mechanism.

  • Experiments are carried out to illustrate the efficiency of the proposed mechanism.

Abstract

The large stroke is usually realized by lowering stiffness along the degrees of freedom, which usually leads to a decrease of stiffness along the degrees of constraint. A high stiffness ratio is crucial for reducing the deflections induced by disturbances such as eccentric force and the gravity of the load. Besides, the fatigue life of these mechanisms will be shortened due to the large stress caused by the large deflection. This paper proposed a new guiding mechanism using orthogonally oriented flexures to improve the stiffness along the degrees of constraint and reduce stress concentration. The energy method is utilized to obtain the kinetostatic model of the guiding mechanism by taking the nonlinear deflection into account, based on which the mechanism is optimized by simultaneously considering the topology and size. As compared to the performance of traditional design obtained through the same optimization objective and constraints, the optimal design effectively improves the stiffness along the degrees of constraint, whose accuracy is also validated by the finite element analysis results. Experimental results show that the proposed mechanism increases the stiffness ratio Kaz/Kx by 3.54 times compared to the traditional mechanism.

Introduction

Compliant mechanisms, capable of providing nanometer resolution by eliminating wear, friction and backlash, have been widely used in various precision devices for precision positioning [1], [2], [3], [4], [5], [6], [7], micro-manipulation [8], [9], [10], microgripper [11], and microscopy [12], [13], [14], which are commonly driven by linear actuators such as piezoelectric actuators (PZT) [15], [16], [17] and voice coil motors (VCM) [5,13,18,19]. A PZT actuator exhibits high-speed responses for its high stiffness and can provide large driving forces, while the stroke is limited to 0.1% of its length. Therefore, an amplifying compliant mechanism is usually employed to extend the travel range of the PZT actuator, and a guiding compliant mechanism is designed to minimize the parasitic motions of the amplifying mechanism along its degrees of constraint (DOC) [17,[20], [21], [22], [23].

A VCM provides a larger actuation stroke, but the travel range is limited by the actuation force required by the compliant mechanism. Thus, leaf springs are often chosen for the design of linear guiding mechanisms to reduce the stiffness along the guiding direction [24], [25], [26], [27], [28], [29]. Compliant compound parallelogram mechanisms (CCPM) are the typical guiding mechanisms designed with leaf springs. Hao and Kong used CCPM to design a large-range XY compliant parallel manipulator in Ref. [29], whose motion range reaches 20 × 20 mm. Ref. [25] extended the travel range of a linear-motion mechanism by utilizing the compressed-soft effect of leaf spring to reduce the stiffness along its degrees of freedom (DOF). However, low stiffness along the DOC is also prone to occur in these mechanisms for the large ratio of length to thickness of leaf springs (l/t), which leads to an increase of deflection caused by the disturbing loads. Therefore, the present CCPMs have limited efficiency in some applications with additional loads along the DOCs. To enhance the out-of-plane stiffness of CCPMs, Ref. [29] increased the beam number and utilized spatial compliant legs. Although the out-of-plane stiffness is improved in this way, the driving stiffness is also increased. For the compliant mechanism subjected to torsional moment due to the deviation of driving force from the motion center [30], improving the ratio of stiffness along the DOCs to it along the DOF is a more efficient method to decrease the disturbance displacement.

On the other hand, the maximum stress of compliant elements has a crucial influence on the fatigue life of compliant mechanisms, which have been well researched for the notch flexure hinges in Ref. [31]. The sudden shape change of leaf springs generates notable stress concentration characteristics which enlarged the maximum stress of mechanisms greatly. Therefore, Ref. [32] investigates the scope for stress reduction through shape optimization of the leaf springs, in which the maximum stress is calculated under the small deflection assumption. In fact, the load-deflection relationship of CCPMs presents obvious nonlinearities for the initial internal axial force [26]. The nonlinearity and stress concentration characteristics of leaf springs without corner curves make it difficult to evaluate the maximum stress at the first stage of mechanism design. In order to model the stress of leaf springs in large-stroke applications, a nonlinear model of corner-fillet leaf springs (CFLS) is provided in Ref. [33] in which the induced fillet improved the maximum stress effectively.

Considering the limitations of current design methods for guiding mechanisms, this article proposed a new guiding mechanism utilizing orthogonally oriented CFLSs and hybrid leaf springs (HLSs). Although it is a usual way to neglect the effect of small fillets during design, tiny fillets have limited improvement in the reduction of maximum stress. Thus nonlinear models of CFLSs and HLSs are adopted in this work for the accurate stress design. The nonlinear energy formula of the guiding mechanism is provided to obtain the kinetostatic model by taking the nonlinear deflection of CFLSs and HLSs into account, and the corresponding nonlinear stress is calculated using the nonlinear model. The simultaneous optimal design of topology and size is carried out to minimize the maximum stress and mass of the mechanism by determining the optimal group number and parameters of CFLSs and HLSs.

The main contents of the paper are arranged as follows: Section 2 introduces the design of the new guiding mechanism in detail. The kinetostatic model of the guiding mechanism is established and the nonlinear stress is calculated in Section 3. The optimized design is illustrated in Section 4 and a design case is provided to explain its efficiency. The performance of the optimal design is verified using the finite element analysis (FEA) method in Section 5. Comparison is accomplished in Section 6 to demonstrate the improvement of the proposed mechanism. Experimental results are obtained in Section 7. Conclusions are drawn in the last section of this paper.

Section snippets

Design

Fig. 1 shows several compliant guiding mechanism designs of parallelogram structures. The guiding mechanism utilizing notch flexure hinges (NFHs), as shown in Fig. 1(a), provides high stiffness and high frequency, but the travel range of these mechanisms is limited to several micrometers due to the low deflection capability of NFHs. Leaf-springs provide good compliance for the guiding mechanisms as shown in Fig. 1(b), but the stiffness along the DOC of these guiding mechanisms is smaller than

Analytical modeling of the guiding mechanism

The driving force applied on the guiding mechanism causes remarkable tension stress in the deflected CFLSs and HLSs, leading to stress stiffening of the mechanism along the DOF. Therefore, the load-displacement relationship of the guiding mechanism presents a non-negligible nonlinearity.

Optimization model

The stiffness along the DOC should be large enough to avoid displacement coupling. Maximum stress has a crucial influence on the fatigue life of mechanisms in some high-speed and high-acceleration applications. Therefore, the design objective is to minimize the total mass and maximum stress of the guiding mechanism by determining the optimal parameters of CFLSs and HLSs which satisfy the frequency and stiffness constraints. The optimization objective can be expressed as:Find(n,r1,t1,w1,r2,l2)to

Verification with FEA

An FEA model is built in COMSOL Multiphysics 5.3 by utilizing the optimal parameters determined in Section 4.2 and FEA results are obtained and listed in Table 3.

The deflections along the DOC of a guiding mechanism subjected to a unit force or moment are depicted in Fig. 8. The maximum deflection of the mechanism along the Y-axis and Z-axis are 0.00213 μm and 0.00114 μm when the mechanism is subjected to a unit load along Y-axis and Z-axis, respectively. The maximum deflection of mechanism

Comparison with guiding mechanism without HLSs

Ref. [33] employed CFLSs for a guiding mechanism to improve the maximum stress of beam-based design, showing that the maximum stress of leaf spring is reduced by 33% for the same travel range. The mentioned mechanism, whose schematic diagram is shown in Fig. 10, is optimized to minimize the total mass and maximum stress by determining the optimal parameters r and t with the same constraints as shown in Eq. (43). The optimal results for different group number n are listed in Table 4, which

Experimental results

The guiding mechanism is manufactured for experimental investigations, in which the HLSs are displaced by the thin leaf springs produced by spring steel 65 Mn (the thickness is 0.2 mm) for its high fatigue strength, as shown in Fig. 12. When the leaf springs are disassembled, the proposed design becomes the mentioned guide mechanism shown in Fig. 10. The efficiency of the proposed design is illustrated by measuring the stiffness ratio of the guiding mechanism in two different states (leaf

Conclusions

A new guiding mechanism employing orthogonally oriented CFLSs and HLSs is proposed in this paper to provide a high stiffness ratio along the DOC to it along the DOF and reduce the stress concentration. The nonlinear deflection and maximum stress of the guiding mechanism are investigated for large-stroke applications. The kinetostatic model is obtained by utilizing the energy method for the simultaneous optimal design of topology and size. An optimization design is carried out to minimize the

Declaration of Competing Interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “A compliant guiding mechanism utilizing orthogonally oriented flexures with enhanced stiffness in degrees-of-constraint”.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 51875108, 51905107, 51975128, and 61973093).

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