Recent designs of soft robots and nano robots feature locomotion mechanisms that

entail orchestrating changes to intrinsic curvature or length to enable the robot’s limbs to

either stick, adhere, or slip on the robot’s workspace. The resulting locomotion mechanism

has several features in common with peristaltic locomotion that can be found in the animal

world. One of the purposes of this dissertation is to examine the feasibility of, and design

guidelines for, a locomotion mechanism that exploits the control of intrinsic curvature on

a rough surface featuring stick, slip, and adhesion interaction. Our work complements the

ever-increasing body of work on soft robots that is primarily focused on the design and

fabrication of these systems. Modeling and analyzing these robots is challenging because

of the difficulties in faithfully modeling the flexible nature of their components.

The study of locomotion presented in this dissertation is composed of two parts. First,

we consider the simplest possible model for a soft robot. The resulting model is a lumped

parameter system featuring a pair of mass particles and a spring with a variable natural

length. By appropriately varying the natural length as a function of time ℓ0(t), we show

how locomotion can be achieved and examine the energy efficiency for a variety of choices

of ℓ0(t). We then take the lessons gained from this model and use them to understand

the locomotion of a block that is propelled on a rough surface with the aid of a flexible

arm. Our analysis of the rod-based model for this system focuses on the development of a

structurally stable mechanism to move the block. This analysis exploits recent results on

stability of adhered rods that we supplement with a new discretized stability criterion.

Beyond locomotion, soft robots have the ability to gently grip and maneuver objects

with open-loop kinematic control. Guided by several recent designs and implementations

of soft robot hands, we exploit our earlier works on locomotion and analyze a rod-based

model for the fingers in the hand of a soft robot. We show precisely how gripping is

achieved and how the performance can be affected by varying the system’s parameters. The

designs of interest feature pneumatic control of the soft robot and we model this actuation

as a varying intrinsic curvature profile of the rod. Our work provides a framework for the

theoretical analysis of the soft robot and the resulting analysis can also be used to develop

some design guidelines.

This report presents an algorithm for the detection of collision between two vehicles. The theory of a pseudo-rigid body is used to facilitate the development of the algorithm. The report concludes with examples of four vehicular impact scenarios to illustrate the applicability of the proposed algorithm.

Engineering and everyday experience alike provide countless examples of deformable objects coming into contact with effectively rigid objects, from a belt stretched between pulleys in an automobile engine to a ball bouncing on a blacktop. But despite the ubiquity of such systems, we have little in the way of a fundamental understanding of the dynamics they can be expected to display. The main obstacle to deeper understanding is mathematical: the unilateral constraint of contact creates free boundaries, and free-boundary-value problems are inherently nonlinear, even if the underlying differential equations are themselves linear. This dissertation explores the dynamics of contact in several prototypical problems inspired by engineering applications such as indentation testing, offshore oil exploration and production, and microelectromechanical systems (MEMS) design.

The first major thrust of the present work is the linear vibration analysis of a beam contacting a flat surface due to combined gravity and adhesion. In analyzing this problem we develop a technique for appropriately linearizing the conditions at a free boundary. We then extend the technique to study the nonlinear vibrations of the gravity-only problem using a second-order perturbation analysis, which shows that contact generates a rich array of nonlinear resonances. The results show good agreement with numerical solutions from a special finite element method that precisely tracks the free boundary. We conclude by using the gap function formalism common in computational contact mechanics to demonstrate that the same pattern of resonances can be expected to arise in a more general class of problems.

Having studied a problem involving a one-dimensional continuum, we shift attention to one with a two-dimensional continuum: an electrostatically actuated plate contacting a charged, dielectric-coated substrate. We use a variational method to derive one model in which the dielectric thickness is finite, and the other in which the thickness is small. The latter corresponds to a common type of surface adhesion. We formulate the linear stability equations for both models and characterize their equilibria in the case of a circular actuator before adopting an approximation from dynamic fracture mechanics to study the dynamics of the thin-dielectric model, which display some unique mathematical properties, including finite-time blow-up. Finally, we discuss application of the model to the problem of vibration-assisted stiction repair.

This work incorporates many analytical and computational tools, from configurational mechanics, to perturbation theory, to arbitrary Lagrangian-Eulerian finite element methods, and represents a first step toward the development of rules-of-thumb for the design of vibration-critical mechanical systems with contact constraints.