Animals can utilize elastic energy stored in biological springs to execute fast and
powerful movements that surpass the limitations of muscle (Burrows, Groeneberg). Some
biological springs act like catapults to amplify power by decreasing the time which work is done
to release energy in relation to the amount of time work is done to store energy (Patek, Burrows).
Though many studies suggest that the biological springs used by these animals are capable of
generating these extremely fast movements, there is still work to be done to address the
constraints that these animals face as well as how these constraints affect the biological springs.
Therefore, in order to understand the evolution of extremely fast and powerful movements,
I will study how the biological constraints of these animals affect the parameters of elastic
energy storage mechanisms as well as what possible strategies animals use to deal with
these restraints.
Although utilizing spring systems to generate fast movements circumvents the limitations
of muscular contractions, loading the spring with energy does not. This may become
problematic for animals which need to both load the spring and execute a movement in a very
small amount of time. For example, although a spring is able to store more energy as its stiffness
increases, a spring that is too stiff could potentially be disadvantageous to the majority of
invertebrates utilizing spring systems to either catch prey or escape predation. I hypothesize that
since the compression of the spring is constrained by the power output of muscle, a tradeoff
between force generation by a stiff spring and the time required to execute a predatory strike or
antipredatory maneuver could predict the optimum spring stiffness for any given organism.
Another parameter which plays an important role in biological springs is the ratio of
energy storage to volume of elastic material. The reasons for maximizing the ratio of energy
storage to volume of material are twofold. First of all, arthropods invest considerable energy to
build and calcify these elastic elements during each molt cycle (CITE), therefore there is a high
demand to minimize the volume of elastic material. Secondly, since these biological springs are
being used to actuate fast movements, it is advantageous to reduce the total weight of material
used to create the spring. For these reasons I hypothesize that biological spring systems will
concentrate elastic energy by maximizing energy storage while minimizing the volume of
material that stores this energy.
It is also possible to modify a biological spring’s stiffness by modifying the shape of the
spring. A previous study suggests that in order to maintain a constant spring stiffness, mantis
shrimp may be able to modulate either the material stiffness or the material shape as they grow
larger (Zack). Given that these biological springs can take on many different forms from arches
to beams (Burrows, Patek), I hypothesize that variations in morphology determine the elastic
energy storage capacity of biological springs.
To test these hypotheses, I will study mantis shrimp, which are able to store elastic
energy in their striking appendages and use this ability to attack prey items with incredible
speeds and forces often exceeding 20 m/s and 400 N per strike (cite Patek). Previous research
has looked at the spring mechanics of mantis shrimp appendages and suggested that in general,
spring stiffness is relatively constant within species (Zack, Patek in prep). Mantis shrimp are
good model organisms to study elastic energy mechanisms not only because of their impressive
strike performance, but also because of the wide variety of sizes and shapes observed in the
striking appendage across species. Although “spearer” species generally have elongated
appendages with sharpened barbs to pierce prey and “smasher” species generally have more
stout-shaped appendages with calcified regions to hammer prey, appendages across species
maintain common structures hypothesized to store elastic energy: the highly-calcified regions
known as the ventral bars and the less-calcified dorsal hyperbolic paraboloid saddle. By
studying the spring mechanics across these differing mantis shrimp morphologies, we can begin
to understand how these animals circumvent previously stated restraints of speed, and material.
First, I will collect kinematic data from mantis shrimp strikes from 5 “spearer” and 5
“smasher” species in order to calculate the optimum stiffness for each species. To do this, I will
use high speed video to measure the time and distance required to fully compress the spring.
Then I will dissect the muscle from the appendage to take physiological measurements of the
muscle to determine the maximum power the muscle can produce. With these measurements, I
can calculate the force exerted by the muscle and use this to estimate the stiffness of the spring.
For each species, I will then conduct materials tests on the appendages to measure spring
stiffness using the materials testing machine in Professor Sheila Patek’s lab (UMass Amherst)
and compare the measured results with my prediction for each of the 10 species.
Second, I will create micro computed tomography (micro-CT) scans of all species in this
study at the Harvard University Center for Nanoscale Systems. In collaboration with Betsy
Dumont (UMass Amherst) I will use these scans to recreate 3 dimensional volumetric meshes of
the appendages, and simulate compression of the springs using finite element analysis (FEA) to
measure strain energy, the amount of energy needed to deform the structure. These volumetric
meshes are built of thousands of smaller tetrahedral bricks. Since the model is built of small and
simple parts, we can use FEA, an engineering technique used to solve complex systems of
equations, to compute strain energy of each individual brick during spring compression. For
each model, I can then calculate the percent volume of bricks which account for 100% of the
strain energy down to 50% of the strain energy in increments of 1% in order to assess any
patterns of energy maximization with associated volume minimization.
Third, to assess the effect of morphology decoupled from material properties I will
conduct finite element analyses on all volumetric meshes assigning the same material properties
to every part of the model. Then, I will subgroup the model into different parts representing the
ventral bars and the saddle, I will dissect out the selected parts from real appendages, and
conduct dynamic materials tests in order to measure the material properties of each of these parts.
I will then be able to do another round of finite element analyses with the same models, except
this time assign differential material properties according to the physical tests. This will reveal
patterns of the sole effect of morphology on strain energy.
Broader Impacts: By studying the appendages of mantis shrimp at this level, we will gain
a better understanding of how mantis shrimp deal with biological constraints. By understanding
the limitations of springs and possible solutions to these limitations, integrated spring systems
could be designed to be less heavy and more cost effective. This is especially of interest to
people designing jumping microrobots (CITE). In addition, this research will provide a more
extensive understanding of the evolution of elastic energy systems and a stepping stone to
studying the role of morphology in the elastic energy storage of other organisms. This project
will foster collaborative work with other departments. For example, more computationally
intensive analyses can be done with the assistance of Professor Ian Grosse in the department of
Mechanical and Industrial Engineering (UMass Amherst). Additionally, this project will provide
opportunities for undergraduates to enter in a highly interdisciplinary research frame work
through the Biology Undergraduate Research Apprenticeship, a new program at UMass Amherst
designed to provide research opportunities to undergraduate students.