Designing higher-order angular-displacement amplifiers for piezoelectric actuators using infinitesimal mechanisms

Abstract Displacement amplifiers are essential components in precision engineering and piezoelectric-based systems. However, there are only a few types available amplifiers in both academia and industry, with limited amplification ratios, such as lever-type and bridge-type amplifiers. This paper presents a novel approach for designing higher-order angular-displacement amplifiers, utilizing the concept of infinitesimal mechanisms and shakiness. In this framework, traditional amplifiers such as bridge amplifiers are viewed as special cases of lower-order amplifiers. The paper begins by discussing planar 3-RPR platforms and their variations in the design of angular-displacement amplifiers. These amplifiers operate near a critical point called shaky point where the corresponding mechanisms become infinitesimal mechanisms with infinitesimal rotational mobility when all the linear actuators are locked. Solutions of higher-order shakiness are presented, which are based on the method of higher-order analysis of screws and curvature theory. Using singular value decomposition of the input-output Jacobian, it is theoretically demonstrated that a one-dimensional displacement-amplification subspace (DAS) exists near this shaky point. Further finite kinematic analysis reveals that the configuration spaces exhibit steep changes near the critical point. It is within this space that the mechanisms exhibit amplification effects. Four distinct amplification curves are identified, depending on the parity of the shakiness order and whether the initial configuration is rotational or translational, instantaneously. Amplifiers in translational positions also exhibit novel cusp mechanisms. Parameter analysis of the compliant versions of these amplifiers are also explored. Optimal bias angles of the platforms are identified, which provide the best amplification ratios for given inputs. Finally, a third-order compliant amplifier is prototyped for experiment verification. The experiment shows a 0.0006 times link-length input can generate a 4° rotation, demonstrating a clear superiority in amplification ratio over traditional amplifiers. The proposed amplifiers are particularly well-suited for large bending deformation applications, such as lightweight soft robots and morphing airplane wings actuated by piezoelectric actuators.