The paper deals with compliant mechanisms with variable stiffness behavior. Mechanisms with such behavior have received increasing attention in recent years, especially in the context of variable stiffness actuators. In the work presented here, variable stiffness behavior is achieved by targeted application of prestressing forces. An efficient optimization-based method based on linear programming is presented to identify suitable force application points, force magnitudes, and -directions. The performance of the method is numerically and experimentally demonstrated on a compliant mechanism with one translational degree of freedom. The demonstrator is appropriate for application in the research field of variable stiffness actuators. In the experimental investigation, particular emphasis is given on a tailored force-displacement characteristic of the mechanism. The required prestressing forces are realized by a pneumatic artificial muscle. Its modeling and precise control is discussed in detail within the experimental part of the paper. Both the results of the numerical and the experimental investigation demonstrate the potential for precise variation of the stiffness behavior with the presented approach.
BatheK-J (1982) Finite element procedures for solids and structures - LinearAnalysis. In: BatheK-J (ed.) Finite Element Procedures. Upper Saddle River, NJ: Prentice-Hall, pp.148–214.
2.
BažantZPCedolinL (2010) Stability of Structures. Singapore: World Scientific.
3.
BleicherASchlaichMFujinoY, et al. (2011) Model-based design and experimental validation of active vibration control for a stress ribbon bridge using pneumatic muscle actuators. Engineering Structures33(8): 2237–2247.
4.
ChenW-FLuiEM (1987) Structural Stability: Theory and Implementation. Upper Saddle River, NJ: Prentice Hall.
5.
DantzigGOrdenAWolfeP (1955) The generalized simplex method for minimizing a linear form under linear inequality restraints. Pacific Journal of Mathematics5(2): 183–195.
6.
EastmanFS (1937) The design of flexure pivots. Journal of the Aeronautical Sciences5(1): 16–21.
7.
GöttertMNeumannR (2007) Bahnregelung servopneumatischer Antriebe – ein Vergleich von linearen und nichtlinearen Reglern (Continuous path control of servo pneumatic drives – A comparison of linear and non linear controllers). at - Automatisierungstechnik55(2): 69–74.
HaringxJA (1949) The cross-spring pivot as a constructional element. Flow Turbulence and Combustion1(1): 313.
10.
HasseACampanileLF (2009) Design of compliant mechanisms with selective compliance. Smart Materials and Structures18(11): 115016.
11.
HasseAFranzMMauserK (2017) Synthesis of compliant mechanisms with defined kinematics. In: ZentnerLCorvesBJensenB, et al. (eds) Microactuators and Micromechanisms. Cham: Springer International Publishing, pp.227–238.
12.
HasseAZuestICampanileLF (2011) Modal synthesis of belt-rib structures. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science225(3): 722–732.
13.
HawksJCColtonMBHowellLL (2015) A variable-stiffness straight-line compliant mechanism. In: ASME 2015 international design engineering technical conferences and computers and information in engineering conference, Boston, MA, 2–5 August.
HildebrandtANeumannRSawodnyO (2010) Optimal system design of SISO-servopneumatic positioning drives. IEEE Transactions on Control Systems Technology18(1): 35–44.
16.
HildebrandtASawodnyONeumannR, et al. (2002) A flatness based design for tracking control of pneumatic muscle actuators. In: 7th international conference on control, automation, robotics and vision, Singapore, 2–5 December, pp.1156–1161. New York: IEEE.
17.
HoganN (1985) Impedance control: An approach to manipulation: Part III—Applications. Journal of Dynamic Systems Measurement and Control107(1): 17–24.
18.
HowellLL (2001) Compliant Mechanisms. New York, NY: John Wiley & Sons.
19.
ISO 6358 (1989) Pneumatic Fluid Power-Components Using Compressible Fluids Determination of Flow-Rate Characteristics. Geneva: ISO.
20.
JunhoSArmenDK (2006) Generalized Bouc–Wen model for highly asymmetric hysteresis. Journal of Engineering Mechanics132(6): 610–618.
21.
LaffranchiMTsagarakisNCaldwellDG (2011) A compact compliant actuator (CompAct™) with variable physical damping. In: 2011 IEEE international conference on robotics and automation, Shanghai, China, 9–13 May, pp. 4644–4650. New York: IEEE.
22.
MartensMBoblanI (2017) Modeling the static force of a Festo pneumatic muscle actuator: A new approach and a comparison to existing models. Actuators6: 33.
23.
MauserKHasseA (2020) How to prestress compliant mechanisms for a targeted stiffness adjustment. Smart Materials and Structures29(8): 085021.
24.
MehrotraS (1992) On the implementation of a primal-dual interior point method. SIAM Journal on Optimization2(4): 575–601.
PrattGAWilliamsonMM (1995) Series elastic actuators. In: Proceedings 1995 IEEE/RSJ international conference on intelligent robots and systems. Human robot interaction and cooperative robots, Pittsburgh, PA, 5–9 August, pp.399–406. New York: IEEE.
27.
PrzemienieckiJS (1985) Theory of Matrix Structural Analysis. New York: Courier Corporation.
28.
SaifMT (2000) On a tunable bistable MEMS-theory and experiment. Journal of Microelectromechanical Systems9(2): 157–170.
29.
SarosiJBiroINemethJ, et al. (2015) Dynamic modeling of a pneumatic muscle actuator with two-direction motion. Mechanism and Machine Theory85: 25–34.
30.
SchindeleD (2013) Einsatz Pneumatischer Muskeln Als Aktoren in Der Robotik. Aachen, Germany: Shaker Verlag.
31.
SchindeleDAschemannH (2012) Model-based compensation of hysteresis in the force characteristic of pneumatic muscles. In: 2012 12th IEEE international workshop on advanced motion control (AMC), Sarajevo, Bosnia and Herzegovina, 25–27 March, pp.1–6. New York: IEEE.
32.
TreaseBPMoonY-MKotaS (2005) Design of large-displacement compliant joints. Journal of Mechanical Design127(4): 788–798.
33.
Vo-MinhTTjahjowidodoTRamonH, et al. (2011) A new approach to modeling hysteresis in a pneumatic artificial muscle using the Maxwell-Slip Model. IEEE/ASME Transactions on Mechatronics16(1): 177–186.
34.
WittrickW (1948) The theory of symmetrical crossed flexure pivots. Australian Journal of Chemistry1(2): 121–134.
35.
WolfSGrioliGEibergerO, et al. (2016) Variable stiffness actuators: Review on design and components. IEEE/ASME Transactions on Mechatronics21(5): 2418–2430.
36.
WuYLanC (2014) Design of a linear variable-stiffness mechanism using preloaded bistable beams. In: 2014 IEEE/ASME international conference on advanced intelligent mechatronics, Besancon, France, 8–11 July, pp.605–610. New York: IEEE.
37.
YalcinMUzunogluBAltintepeE, et al. (2013) VNSA: Variable negative stiffness actuation based on nonlinear deflection characteristics of buckling beams. In: 2013 IEEE/RSJ international conference on intelligent robots and systems (IROS), Tokyo, Japan, 3–7 November, pp.5418–5424. New York: IEEE.
38.
ZhaoHHanDZhangL, et al. (2017) Design of a stiffness-adjustable compliant linear-motion mechanism. Precision Engineering48: 305–314.
