Mechanical computing systems have historically faced challenges in efficiently integrating computation and memory functions, often leading to complex designs and limited scalability in applications ranging from micro-electromechanical systems (MEMS) to programmable matter. This study aims to address this issue by introducing a mechanical system based on cellular automata (CA) principles, utilizing a bi-threshold tristable mechanism for implementing nonlinear Boolean functions. The system’s design translates Elementary Cellular Automata (ECA) rules, such as Rule 110, into mechanical motion using compliant multistable mechanisms. Finite Element Analysis (FEA) and pseudo-rigid body simulations validate the operational feasibility of this approach. The results confirm the system’s capability to process complex computational tasks by mechanically embodying specific ECA rules. This development marks a step forward in mechanical computing, offering a more integrated approach to computational material design. The research establishes a methodical design approach, enabling the embodiment of a wide range of Elementary Cellular Automata (ECA) rules within the mechanical framework. This approach extends beyond linearly separable Boolean functions, illustrating a significant advancement in mechanical computing capabilities. The findings provide a basis for future work in scaling the system and exploring its applicability in fields such as programmable matter and intelligent mechanical systems.

In the field of mechanical metamaterials, unconventional physical properties are realized by changing the geometric structure of a unit cell. A metamaterial is composed of numerous unit cells. Researchers have taken it a step further by making a reprogrammable unit cell. A reprogrammable metamaterial has additional elements or mechanisms in the unit cells that allow their properties to be modified. The state of the unit cell corresponds to a physical property. Switching this state requires an external stimulus. Each unit cell in the metamaterial requires an external stimulus to realise a distinctive state. To decrease the number of external stimuli for a tessellated structure, a unit cell is required that switches state depending on stored information. The focus of this thesis is to design a state switching mechanism for a single unit cell. Recently developed state dependent switching mechanisms consist of parallel distributed compliant beams connected in the centre. An off-centre actuation of a single beam requires less input force than a beam actuated in the centre. There is no model that can be used to develop a state switching mechanism with the ability to change the position of the connecting element. The connecting element must be flexible to allow for rotation. Therefore, in this thesis a Pseudo-Rigid-Body Model (PRBM) of a single input switching mechanism is developed that includes the off-centre connection to perform an analysis of the key parameters. The model consists of lumped beams to have a clear deformation path. The model is developed in MATLAB and validated with a finite element model (FEM). Additionally, a 3D printed prototype is made and experimentally validated to compare with the PRBM and FEM simulation. This model enables the ability to understand the effect of the flexible connecting segment and the decrease in force magnitude to actuate the system. The geometrical advantage can be tuned through preload and the ratio between the rigid beam segments. The developed model is a powerful tool that can be used to validate the functionality of any set of parameters of a coupled beam contact-based state switching mechanism.