Kinetostatic analysis of 6-DOF compliant platform with a multi-stage condensed modeling method
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ORIGINAL RESEARCH
Kinetostatic analysis of 6-DOF compliant platform with a multi-stage condensed modeling method Chao Lin1
•
Shan Zheng1 • Pingyang Li1 • Mingdong Jiang1
Received: 24 July 2020 / Accepted: 3 September 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Matrix displacement method, based on matrix operation without complex internal force analysis, gives accurate solutions and concise process for the kinetostatic analysis of the compliant mechanisms. However, there are some problems of tedious node numbering in the general matrix displacement method. In this paper, a multi-stage condensed modeling method is proposed to establish kinetostatic model for the compliant platform with complex configurations. Based on the matrix displacement method in structural mechanics and combining with the transfer matrix and coordinate transformation, the complex series–parallel configuration is subjected to multi-stage stiffness equivalent to obtain a concise input/output two-port mechanical network. Then, the proposed method is used to analyze the kinetostatic of the 6-degree-of-freedom (DOF) compliant platform. And a good prediction accuracy is shown by comparison with finite element analysis and experiment. Moreover, the results also show that the hinge thickness and the hinge spacing at the maximum amplification ratio of the bottom platform satisfies the linear condition, which provides implications for the design and optimization of the compliant mechanisms based on the bridge-type amplifiers.
1 Introduction Compliant mechanisms achieve transmission of movement and force by the bending of the flexible member. Compared with traditional rigid body mechanisms, there are some advantages of compliant mechanisms including highly accurate motion, low wear, no friction and compact structure (Howell et al. 2001). Therefore, they have attracted extensive attention in various scientific and industrial applications, such as aerospace technology, MEMS, biomedical engineering, optical engineering and other modern precision engineering fields (Dechev et al. 2006; Hao et al. 2016; Xi et al. 2016; Mallick et al. 2014). However, unlike conventional mechanisms, the challenge of compliant mechanisms is that both kinematics and elastic mechanics need to be considered when designing and analyzing of compliant mechanisms (Ling et al. 2018). Howell, Lobontiu, and other scholars pioneered the analysis of compliance mechanisms. (Howell et al. 2001; Yong et al. 2008; Howell et al. 1996). Among them, Howell & Chao Lin [email protected] 1
State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China
proposed the famous Pseudo Rigid Body Model (PRBM) method (Howell et al. 1996). Subsequent scholars proposed many new analytical methods, for instance, the principle of virtual work (Ling et al. 2016a, b; Choi et al. 2018; Sen et al. 2013), the beam-constraint-model (BCM) (Awtar et al. 2007; Awtar et al. 2010; Ma et al. 2016; Chen et a
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