# ES 240 Problem Set #8, Problem #20 - Project Description

I work in the Microrobotics lab here at Harvard, where we focus on the construction of biomimetic insect-sized microrobots. Traditional machining techniques are insufficient to create parts on this small scale, so we utlize laser-machined composite materials (such as carbon fiber), which are relatively rigid, and thin polymer films, which are relatively flexible. These materials can be sandwiched together in sheets to create compliant flexure joints, analagous to macro-scale revolute joints.

The polymer flexure joints have a bending stiffness that can be calculated by treating the joint as a cantilever beam (k=E*I/L). We are interested in being able to actively modulate the stiffness of a flexure, as this effects the dynamics of an entire robot (for example, we want to be able to asymmetrically control the wing flapping angle on a microrobotic fly in order to produce a net body torque for flight stabilizations). One possible method of doing this is to coat the polymer flexure with a thin layer of shape-memory alloy (SMA) material. SMAs experience a larger change in elastic properties when heated by an electric current. Thus, changing the modulus of elasticity E of the SMA would change the total equivalent stiffness of the entire flexure, k, giving us the control we desire.

The analysis is not that simple, however, because SMA's typically also undergo a very large strain when heated. Thus, if the SMA is rigidly bonded to the polymer film (substrate), which would not contract when heated, this could result in high residual stresses and possible delamination of the SMA film as it attempts to contract but is held in place by the substrate. This is similar to one of our homework problems for plate bending theory.

Thus, our project will consist of two parts - first, composite cantilever beam theory will be used to analyze the effects of the stiffness change of the SMA on the equivalent bending stiffness of the beam. This analysis will take into effect the change in material properties, but not the large deformation, of the SMA. The second part of the project will consist of an analytical and/or finite element model of the thin film/substrate plate problem. This will determine if SMAs are a reasonable solution to this problem, or if it is likely that the film will delaminate or otherwise cause structural failure due to the very large thermal strain.