Analytical modeling, optimization and testing of a compound bridge-type compliant displacement amplifier

Qingsong Xu, Yangmin Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

246 Citations (Scopus)


This paper investigates a flexure-based compound bridge-type (CBT) displacement amplifier for piezoelectric drives. In addition to the advantages of large amplification ratio and compact size, the CBT amplifier has a larger lateral stiffness and is more suitable for actuator isolation and protection than the ordinary bridge-type amplifier. An analytical model for amplification ratio calculation is established based on the Euler-Bernoulli beam theory because other simple theoretical approaches cannot predict the ratio properly. The reason why those approaches fail is discovered by resorting to the elastic model. The input stiffness and resonance frequency of the amplifier are also analytically modeled and verified by finite-element analysis (FEA). The derived models are utilized to optimize the amplifier structure through particle swarm optimization (PSO) to obtain a large resonance frequency subject to other performance constraints. The performances of the fabricated amplifier with optimized parameters are confirmed by both FEA simulation and experimental studies. Because an output displacement over 1 mm is achieved by the designed amplifier, it is employable to develop micro/nanopositioning stages with a cubic millimeter sized workspace.
Original languageEnglish
Pages (from-to)183-200
Number of pages18
JournalMechanism and Machine Theory
Issue number2
Publication statusPublished - 1 Feb 2011
Externally publishedYes


  • Compliant mechanisms
  • Finite-element analysis
  • Flexure hinges
  • Mechanical amplifier
  • Optimum design
  • Piezoelectric actuation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Computer Science Applications
  • Bioengineering


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