Compliant Manipulators

Reference work entry


Compliant manipulators are advanced robotic systems articulated by the flexure joints to deliver highly repeatable motion. Using the advantage of elastic deflection, these flexure joints overcome the limitations of conventional bearing-based joints such as dry friction, backlash, and wear and tear. Together with high-resolution positioning actuators and encoders, the compliant manipulators are suitable ideal candidates for micro-/nanoscale positioning tasks. This chapter presents the relevant knowledge of several fundamental topics associated with this advanced technology. After reviewing its evolution and applications, the principal of mechanics is used to explain the limitations of these manipulators. Subsequent topic covers various theoretical modeling approaches that are generally used to predict the deflection stiffness of flexure joints and stiffness characteristics of compliant manipulators. Next, various fundamental design concepts for synthesizing the compliant mechanism will be introduced and several examples are used to demonstrate the effectiveness of these concepts. The topic on actuation, sensing, and control summarizes the types of high-resolution actuators and sensors which the compliant manipulators use to achieve high-precision positioning performance. Performance trade-offs between various actuators and among different sensors are discussed in detail. With this relevant knowledge, this chapter serves as a guide and reference for designing, analyzing, and developing a compliant manipulator.


Compliant Mechanism Leaf Spring Torsional Spring Optical Encoder Thermal Actuator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Bacher JP (2003) Conception de robots de très haute precision á articulation flexibles: interaction dynamique-commande. PhD thesis, Ecole Polytechnique Fdrale de Lausanne (EPFL) (No 2907)Google Scholar
  2. Becker P, Seyfried P, Siegert H (1987) Rev Sci Instrum 58(2):207CrossRefGoogle Scholar
  3. BEI Kimco Magnetics (2014) Linear voice coil actuators. Online: BEI Kimco Magnetics website,
  4. Bellouard Y, Clavel R (2004) Mater Sci Eng A 378, pp 210–215Google Scholar
  5. Bendsoe MP (1989) Struct Optim 1, pp 193–202Google Scholar
  6. Bendsoe MP, Kikuchi N (1988) Comput Methods Appl Mech Eng 71, pp 197–224Google Scholar
  7. Bendsoe MP, Sigmund O (1999) Arch Appl Mech 69, pp 635–654Google Scholar
  8. Bendsoe MP, Aharon BT, Jochem Z (1994) Struct Optim 7(3):141CrossRefGoogle Scholar
  9. Blanding DL (1992) Principles of exact constraint mechanical design. Eastman Kodak, RochesterGoogle Scholar
  10. Boone BG, Bokulic RS, Andrewsa GB, McNutt JR, Dagalakisb N (2002) Optical and microwave communications system conceptual design for a realistic interstellar explorer. In: SPIE international society of optical engineering, Jun, Bellingham, Whatcom County, USA, pp 225–236Google Scholar
  11. Borovic B, Lewis FL, Liu AQ, Kolesar ES, Popa D (2006) J Micromech Microeng 16, pp 1233–1241Google Scholar
  12. Brennen RA, Lim MG, Pisano AP, Chou AT (1990) Large displacement linear actuator. In: 4th Technical Digest., IEEE Solid-State Sensor and Actuator Workshop, 4–7 Jun, Hilton Head Island, South Carolina, USA, pp 135–139Google Scholar
  13. Byrd PF, Fredman MD (1954) Handbook of elliptic integrals for engineers and physicists. Springer, BerlinCrossRefMATHGoogle Scholar
  14. Canfield SL, Beard JW, Lobontiu N, O’Malley E, Samuelson M, Paine J (2002) Int J Robot Autom 17:63Google Scholar
  15. Chapman C, Jakiela M (1996) ASME J Mech Des 118(1):89CrossRefGoogle Scholar
  16. Chen SC, Culpepper ML (2006) Precis Eng 30:314CrossRefGoogle Scholar
  17. Chen KS, Trumper DL, Smith ST (2002) Precis Eng 26:355CrossRefMATHGoogle Scholar
  18. Chiou JC, Lin YJ (2005) J Micromech Microeng 15, pp 1641–1648Google Scholar
  19. Chu DN, Xie YM, Hira A, Steven GP (1997) Finite Elem Anal Des 24, pp 191–212Google Scholar
  20. Comtois JH, Bright VM (1996) Surface micromachined polysilicon thermal actuator arrays and applications. In: Sold-state sensor and actuator workshop, 2–6 Jun, Hilton Head, South Carolina, USA, pp 242–253Google Scholar
  21. Comtois JH, Bright VM (1997) Sensors and Actuators A 58, pp 19–25Google Scholar
  22. Culpepper ML, Anderson G (2004) Precis Eng 28:469CrossRefGoogle Scholar
  23. Deslattes RD (1969) Appl Phys Lett 15(11):386CrossRefGoogle Scholar
  24. Dong L, Arai F, Fukuda T (2000) 3D Nanorobotic Manipulation of Nano-order Objects inside SEM. In: 2000 International symposium on micromechatronics and human science, 22–25 Oct, Nagoya Congress Center and Nagoya Municipal Industrial Research Institute, Japan, pp 151–156Google Scholar
  25. Dowling NE (1993) Mechanical behavior of materials. Prentice Hall, Upper Saddle RiverGoogle Scholar
  26. Fite K, Goldfarb M (1999) In: 1999 I.E. international conference on robotics and automation, Detroit, pp 2122–2127Google Scholar
  27. Forrest PG (1962) Fatigue of metals. Pergamon Press, ElmsfordGoogle Scholar
  28. Frisch FR (1962) Flexible bars. Butterworth, Washington, DCMATHGoogle Scholar
  29. Fukada S, Nishimura K (2007) Int J Precis Eng Manuf 8:49Google Scholar
  30. Gao P, Swei SM, Yuan Z (1999) Nanotechnology 10:394CrossRefGoogle Scholar
  31. H2W Technologies (2014) Voice coil linear actuators. Online: H2W Technologies website,
  32. Haberland R (1978) In: Symposium on gyroscope technology, Deutsche Gesellschaft fuer Ortung und Navigation, Duesseldorf/Bochum, pp 18–19Google Scholar
  33. Hale LC (1999) Principles and techniques for designing precision machines. PhD thesis, Massachusetts Institute of Technology (MIT)Google Scholar
  34. Han CS, Hudgens JC, Tesar D, Traver A (1991) In: 1991 IEEE/RSJ international conference on intelligent robots and systems, Osaka, pp 1153–1162Google Scholar
  35. Helmer P (2006) Conception systmatique de structures cinmatiques orthogonales pour la microrobotique. PhD thesis, Ecole Polytechnique Fdrale de Lausanne (EPFL) (No 3365)Google Scholar
  36. Heidenhain (2014) Optical sensor. Online: Heidenhain Corporation website,
  37. Henein S (2000) Conception des structures articules guidages flexibles de haute prcision. PhD thesis, Ecole Polytechnique Fdrale de Lausanne (EPFL) (No 2194)Google Scholar
  38. Henein S (2006) Flexure-based mechanism for high precision. In: Technical tutorial notes of 6th International conference of the European society for precision engineering & nanotechnology, May, Vienna, Austria, pp 32–37Google Scholar
  39. HEPHAIST S (2014) Spherical rolling joint SRJ series. Online: Hephaist Sekio website,
  40. Her I, Chang JC (1994) In: 23rd ASME biennial mechanisms conference on machine elements and machine dynamics, pp 517–525Google Scholar
  41. Hesselbach J, Pittschellis R, Hornbogen E, Mertmann M (1997) Shape memory alloys for use in miniature grippers. In: 2nd International Conference on Shape Memory and Superelastic Technologies, 2–6 Mar, Pacific Grove, California, USA, pp 251–256Google Scholar
  42. Ho HL, Yang GL, Lin W (2004) In: 2003/2004 international conference on precision engineering, Singapore, pp 133–140Google Scholar
  43. Howell LL (2001) Compliant mechanism. Wiley, New YorkGoogle Scholar
  44. Howell LL, Midha A (1994) ASME J Mech Des 116:280CrossRefGoogle Scholar
  45. Howell LL, Midha A, Norton TW (1996) ASME J Mech Des 118:126CrossRefGoogle Scholar
  46. Hudgens JC, Tesar DA (1988) In: 20th biennial ASME mechanisms conference, Kissimmee, pp 29–37Google Scholar
  47. Hung ES, Senturia SD (1999) J Micromech Syst 8, pp 497–505Google Scholar
  48. Jones RV (1951) J Sci Instrum 28(2):38CrossRefGoogle Scholar
  49. Jones RV (1952) J Sci Instrum 29:345CrossRefGoogle Scholar
  50. Jones RV (1955) J Sci Instrum 33(6):245CrossRefGoogle Scholar
  51. Jones RV (1956) J Sci Instrum 33(7):279CrossRefGoogle Scholar
  52. Jones RV (1962) J Sci Instrum 39:193CrossRefGoogle Scholar
  53. Jones RV (1988) Instruments and experiences; papers on measurement and instrument design. Wiley, Chichester/New YorkGoogle Scholar
  54. Juvinall RC (1967) Stress, strain, and strength. McGraw-Hill, New YorkGoogle Scholar
  55. Jywe WY, Jeng YR, Liu CH, Teng YF, Wu CH, Wang HS, Chen YJ (2008) Precis Eng 32(4):239CrossRefGoogle Scholar
  56. Kimball LW, Tsai DD, Maloney J (2000) In: 2000 ASME design engineering technical conferences, Baltimore, pp DETC00/MECH-14,116Google Scholar
  57. Lee CW, Kim SW (1997) Precis Eng 21:113CrossRefMATHGoogle Scholar
  58. Lion Precision (2014) Capacitive sensor. Online: Lion Precision website,
  59. Liu L, Tan KK, Chen S, Teo CS, Lee TH (2013) IEEE Trans Ind Inform 9(2):859CrossRefGoogle Scholar
  60. Lobontiu N (1962) Compliant mechanisms: design of flexure hinges. CRC Press, Boca RatonGoogle Scholar
  61. Lobontiu N, Paine JSN, O’Malley E, Samuelson M (2002) Precis Eng 26:183CrossRefGoogle Scholar
  62. Lobontiu N, Garcia E, Hardau M, Bal N (2004) Rev Sci Instrum 75:4896CrossRefGoogle Scholar
  63. Lum GZ, Teo TJ, Yang GL, Yeo SH, Sitti M (2013) In: IEEE/ASME international conference on advanced intelligent mechatronics, Wollongong, vol 1, pp 247–254Google Scholar
  64. Mamin HJ, Abraham DW, Ganz E, Clark J (1985) Rev Sci Instrum 56:2168CrossRefGoogle Scholar
  65. Marin J (1962) Mechanical behavior of engineering materials. Prentice Hall, Upper Saddle RiverGoogle Scholar
  66. Mclnroy JE, Hamann JC (2000) IEEE Trans Robot Autom 16:372CrossRefGoogle Scholar
  67. Mclnroy JE, O’Brien JF, Neat GW (1999) IEEE/ASME Trans Mech 4:91CrossRefGoogle Scholar
  68. Merlet JR (2000) Parallel robot. Kluwer Academic, DordrechtCrossRefGoogle Scholar
  69. Motsinger RN (1964) In: Stein PK (ed) Measurement engineering. Stein Engineering Services, Phoenix, chap. 11Google Scholar
  70. Mukhopadhyay D, Dong J, Pengwang E, Ferreira P (2008) A SOI-MEMS-based 3-DOF planar parallel-kinematics nanopositioning stage. Sensors and Actuators A, 147, pp 340–351CrossRefGoogle Scholar
  71. Nishimura K (1991) Rev Sci Instrum 62(8):2004CrossRefGoogle Scholar
  72. Norton R (2000) Machine design, an integrated approach. Prentice Hall, Upper Saddle RiverGoogle Scholar
  73. Oiwa T, Hirano M (1999) Jpn Soc Precis Eng 65:1425CrossRefGoogle Scholar
  74. Ouyang PR, Tjiptoprodjo RC, Zhang WJ, Yang GS (2008) Int J Adv Manuf Technol 38(5–6):463CrossRefGoogle Scholar
  75. Paros JM, Weisbord L (1965) How to design flexure hinges, Mach Des 37:151–156Google Scholar
  76. Pham HH, Chen IM (2005) Precis Eng 29(4):467CrossRefGoogle Scholar
  77. Physik Instrumente GmbH, (2014) PICMA stack multilayer piezo actuators. Online: Physik Instrumente website,
  78. Portman VT, Sandler BZ, Zahavi E (2000) IEEE Trans Robot Autom 16:629CrossRefGoogle Scholar
  79. Qiu J, Lang JH, Slocum AH, Strumpler R (2003) A high-current electrothermal bistable MEMS relay. In: IEEE 16th annual international conference on micro electro mechanical systems, 19–23 Jan, Kyoto, Japan, pp 64–67Google Scholar
  80. Reynaerts D, Peirs J, Brussel HV (1995) J Micromech Microeng 5, pp 150–152Google Scholar
  81. Rosa MA, Dimitrijev S, Harrison HB (1998) Electron Lett 34, pp 1787–1788Google Scholar
  82. Rozvany GIN (1976) Optimal design of flexural systems. Pergamon, OxfordGoogle Scholar
  83. Rozvany GIN (1995) Structural design via optimality criteria. Kluwer, DordrechtGoogle Scholar
  84. Ryu JW, Gweon DG, Moon KS (1997) Precis Eng 21:18CrossRefGoogle Scholar
  85. Seugling RM, LeBrun T, Smith ST, Howard LP (2002) Rev Sci Instrum 73:2462CrossRefGoogle Scholar
  86. Shigley JE, Mischke CR (2001) Mechanical engineering design, 6th edn. McGraw-Hill, New YorkGoogle Scholar
  87. Shigley JE, Mitchell LD (1983) Mechanical engineering design, 4th edn. McGraw-Hill, New YorkGoogle Scholar
  88. SIOS (2014) Laser interferometry sensor. Online: SIOS GmbH website,
  89. Slocum AH (1992) Precision machine design. Prentice Hall, Englewood CliffGoogle Scholar
  90. Smith ST (2000) Flexure: elements of elastic mechanisms. Gordon and Breach Science Publishers, LondonGoogle Scholar
  91. Smith ST, Chetwynd DG, Bowen DK (1987) J Phys E Sci Instrum 20:977CrossRefGoogle Scholar
  92. Speich J, Goldfarb M (2000) Robotica 18:95CrossRefGoogle Scholar
  93. Stroman RO (2006) Actuator trade-off analysis for darpa/boss prototype. Memorandum report, Naval Research Lab, Chemical Dynamics and Diagnostics Brach, Washington, DCGoogle Scholar
  94. Sun Y, Piyabongkarn D, Sezen A, Nelson BJ, Rajamani R, Schoch R, Potasek DP (2002) In: 2002 IEEE/RSJ international conference on intelligence robots and systems, EPFL, Lausanne, pp 1796–1801Google Scholar
  95. Tai K, Akhtar S (2005) Struct Multidiscip Optim 30(2):113CrossRefGoogle Scholar
  96. Tan KK, Lee TH, Zhou HX (2001) IEEE/ASME Trans Mechatron 6:428CrossRefGoogle Scholar
  97. Tang WC, Chong TU, Nguyen H, Howe RT (1989) Sens Actuat 20, pp 25–32Google Scholar
  98. Teo TJ, Chen IM, Yang GL, Lin W (2008) Nanotechnology 19:315501CrossRefGoogle Scholar
  99. Teo TJ, Yang GL, Lin W (2010) A 3-DOF spatial-motion flexure-based parallel nano-manipulator with large workspace and high payload for UV nanoimprint lithography application. In: 10th international conference of European society for precision engineering and nanotechnology, May, Delft, Netherland, pp 360–363Google Scholar
  100. Teo TJ, Chen IM, Yang GL, Lin W (2010b) Precis Eng 34(3):607CrossRefGoogle Scholar
  101. Teo TJ, Lum GZ, Yang GL, Yeo SH, Sitti M (2013) In: 13th international conference of European society for precision engineering and nanotechnology, vol 1, BerlinGoogle Scholar
  102. Toshiyoshi H, Fujita H (1996) J Micromech Syst 5(4):231CrossRefGoogle Scholar
  103. Tsai LW (1999) Robot analysis: the mechanics of serial and parallel manipulators. Wiley, New YorkGoogle Scholar
  104. Tseytlin YM (2002) Rev Sci Instrum 73:3363CrossRefGoogle Scholar
  105. Tsou C, Lin WT, Fan CC, Chou BCS (2005) J Micromech Microeng 15, pp 855–860Google Scholar
  106. Tuttle SB (1967) Mechanisms for engineering design. Wiley, New York, chap. 8Google Scholar
  107. Wang SC, Hikita HKH, Zhao YS, Huang Z, Ifukube T (2003a) Mech Mach Theory 38:439CrossRefMATHGoogle Scholar
  108. Wang MY, Wang X, Guo D (2003) Comput Methods Appl Mech Eng 192, pp 227–246Google Scholar
  109. Xie YM, Steven GP (1993) Comput Struct 49, pp 885–896Google Scholar
  110. Xu W, King T (1996) Precis Eng 19:4CrossRefGoogle Scholar
  111. Yang GL, Teo TJ, Lin W, Kiew CM, Ho HL (2008) A flexure-based planar motion parallel nanopositioner with partially decoupled kinematic architecture. In: 8th international conference of European society for precision engineering and nanotechnology, May, Zurich, Switzerland, pp 160–165Google Scholar
  112. Yang GL, Teo TJ, Chen IM, Lin W (2011) In: 2011 I.E. international conference on robotics and automation, Shanghai, pp 2751–2756Google Scholar
  113. Yi BJ, Chung GB, Na HY, Kim WK, Suh IH (2003) IEEE Trans Robot Autom 19:604–612CrossRefGoogle Scholar
  114. Yong YK, Lu TF (2009) Mech Mach Theory 44:1156CrossRefMATHGoogle Scholar
  115. Yong YK, Lu TF, Handley DC (2008) Precis Eng 32(2):63CrossRefGoogle Scholar
  116. Zhang B, Zhu Z (1997) IEEE/ASME Trans Mechatron 2:22CrossRefGoogle Scholar
  117. Zhu Y, Corigliano A, Espinosa HD (2006) J Micromech Microeng 16, pp 242–253Google Scholar
  118. Zuo L, Landsiedel N, Prakash M, Kartik M (2003) Design of six-axis nano-manipulator based on compliant mechanism. Technical report, Massachusetts Institute of Technology (MIT)Google Scholar

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© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Mechatronics GroupSingapore Institute of Manufacturing TechnologySingaporeSingapore
  2. 2.Institute of Advanced Manufacturing, Ningbo Institute of Materials Technology and Engineering of the Chinese Academy of SciencesZhenhai District, NingboPeople’s Republic of China
  3. 3.School of Mechanical and Aerospace EngineeringNanyang Technological UniversitySingaporeSingapore

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