The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the past 15years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parametrizations, namely, the frame element-based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, and the ability to converge from an unbiased uniform initial guess are analyzed. Some observations and recommendations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.
This paper is concerned with grasping biological cells in aqueous medium with miniature grippers that can also help estimate forces using vision-based displacement measurement and computation. We present the design, fabrication, and testing of three single-piece, compliant miniature grippers with parallel and angular jaw motions. Two grippers were designed using experience and intuition, while the third one was designed using topology optimization with implicit manufacturing constraints. These grippers were fabricated using different manufacturing techniques using spring steel and polydimethylsiloxane (PDMS). The grippers also serve the purpose of a force sensor. Toward this, we present a vision-based force-sensing technique by solving Cauchy's problem in elasticity using an improved algorithm. We validated this technique at the macroscale, where there was an independent method to estimate the force. In this study, the gripper was used to hold a yeast ball and a zebrafish egg cell of less than 1 mm in diameter. The forces involved were estimated to be about 30 and 10 mN for the yeast ball and the zebrafish egg cell, respectively.Index Terms-Cauchy's problem, mesoscale manufacturing, microgripper, topology optimization, vision-based force sensing.
Dynamic responses of structures are random in nature due to the uncertainties in geometry, material properties, and loading. The random dynamic responses can be represented fairly well by stochastic analysis. The methods used for stochastic analysis can be grouped into statistical and non-statistical approaches. Although statistical approaches like Monte Carlo simulation is considered as an accurate method for the stochastic analysis, computationally less intensive yet efficient, simplified non-statistical methods are necessary as an alternative. The present study is an evaluation of a relatively new non-statistical metamodel-based approach known as, HighDimensional Model Representation, with reference to existing response surface methods such as Central Composite Design, Box Behnken Design, and Full Factorial Design, in a dynamic response analysis. The geometry of a reinforced concrete frame is chosen to conduct free vibration and nonlinear dynamic analysis to study the stochastic responses using High Dimensional Model Representation method. This method was found to provide results as good as other methods with less computational effort with regard to the selected case studies.
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