Miniature compliant grippers are designed and developed to manipulate biological cells and characterize them. Apart from grippers, other compliant mechanisms are also demonstrated to be effective in manipulation and characterization. Although scalability and force-sensing capability are inherent to a compliant mechanism, it is important to design a compliant mechanism for a given application. Two techniques based on Spring-lever models and kinetoelastostatic maps are developed and used for designing compliant devices. The kinetoelastostatic maps-based technique is a novel approach in designing a mechanism of a given topology and shape. It is also demonstrated that these techniques can be used to tune the stiffness of a mechanism for a given application. In situations where any single mechanism is incapable of executing a specific task, two or more mechanisms are combined into a single continuum with enhanced functionality. This has led to designs of composite compliant mechanisms. Biological cells are manipulated using compliant grippers in order to study their mechanical responses. Biological cells whose size varies from 1 mm (a large zebrafish embryo) to 10 µm (human liver cells), and which require the grippers to resolve forces ranging from 1 mN (zebrafish embryo) to 10 nN (human cells), are manipulated. In addition to biological cells, in some special cases such as tissue-cutting and cement-testing, inanimate specimens are used to highlight specific features of compliant mechanisms. Two extreme cases of manipulation are carried out to demonstrate the efficacy of the design techniques. They are: (i) breaking a stiff cement specimen of stiffness 250 kN/m (ii) gentle grasping of a soft zebrafish embryo of stiffness 10 N/m. Apart from manipulation, wherever it is viable, the mechanisms are interfaced with a haptic device such that the user’s experience of manipulation is enriched with force feedback. An auxiliary study on the characterization of cells is carried out using a micro¬pipette based aspiration technique. Using this technique, cells existing in different conditions such as perfusion, therapeutic medicines, etc., are mechanically characterized. This study is to qualitatively compare aspiration-based techniques with compliant gripper-based manipulation techniques. A compliant gripper-based manipulation technique is beneficial in estimating the bulk stiffness of the cells and can be extended to estimate the distribution of Young’s modulus in the interior. This estimation is carried out by solving an inverse problem. A previously reported scheme to solve over specified boundary conditions of an elastic object—in this case a cell—is improved, and the improved scheme is validated with the help of macro-scale specimens.

Two inverse problems in elasticity are addressed with motivation from cellular biomechanics. The first application is computation of holding forces on a cell during its manipulation and the second application is estimation of a cell’s interior elastic mapping (i.e., estimation of inhomogeneous distribution of stiffness) using only boundary forces and displacements. It is clear from recent works that mechanical forces can play an important role in developmental biology. In this regard, we have developed a vision-based force-sensing technique to estimate forces that are acting on a cell while it is manipulated. This problem is connected to one inverse problem in elasticity known as Cauchy’s problem in elasticity. Geometric nonlinearity under noisy displacement data is accounted while developing the solution procedures for Cauchy’s problem. We have presented solution procedures to the Cauchy’s problem under noisy displacement data. Geometric nonlinearity is also considered in order to account large deformations that the mechanisms (grippers) undergo during the manipulation. The second inverse problem is connected to elastic mapping of the cell. We note that recent works in biomechanics have shown that the disease state can alter the gross stiffness of a cell. Therefore, the pertinent question that one can ask is that which portion (for example Nucleus, cortex, ER) of the elastic property of the cell is majorly altered by the disease state. Mathematically, this question (estimation of inhomogeneous properties of cell) can be answered by solving an inverse elastic boundary value problem using sets of force-displacements boundary measurements. We address the theoretical question of number of boundary data sets required to solve the inverse boundary value problem.