  Modular Active Cell Robots (MACROs) are a design paradigm for modular robotic
hardware that uses only two components, namely actuators and passive compliant
joints. Under the MACRO approach, a large number of actuators and joints are
connected to create mesh-like cellular robotic structures that can be actuated
to achieve large deformation and shape-change. In this two-part paper, we study
the importance of different possible mesh topologies within the MACRO
framework. Regular and semi-regular tilings of the plane are used as the
candidate mesh topologies and simulated using Finite Element Analysis (FEA). In
Part 1, we use FEA to evaluate their passive stiffness characteristics. Using a
strain energy method, the homogenized material properties (Young's modulus,
shear modulus, and Poisson's ratio) of different mesh topologies are computed
and compared. The results show that the stiffnesses increase with increasing
nodal connectivity and that stretching-dominated topologies have higher
stiffness compared to bending-dominated ones. We also investigate the role of
relative actuator-node stiffness on the overall mesh characteristics. This
analysis shows that the stiffness of stretching-dominated topologies scale
directly with their cross-section area whereas the bending-dominated ones do
not have such a direct relationship.
