In the classic Hill model for muscle contraction, the split between the muscle and tendon is arbitrary and the problem lacks a unique solution. Instead of reformulating the problem to a differential-algebraic equation and solving for a set of initial conditions, a constant tendon length is commonly assumed in musculoskeletal simulation tools. This assumption has not been thoroughly tested and introduces errors of unknown magnitude to the simulations. In this thesis, the contractile element of the Hill model is modelled as a friction clutch in parallel to a viscous damper. This provides an evolution law for the muscle length by which the muscle speed is numerically calculated taking into account a non-zero tendon speed. A simple biceps curl is simulated with the friction clutch model and compared to corresponding commercial musculoskeletal simulations. Overall, the results are similar, in particular for the muscle lengths which are almost identical in every simulation (0.00-0.42% difference). The difference in tendon speed is 0.00-3.26%, with upwards tendencies. In general, the error percentage of the tendon speed appears to decrease by the same amount that the contraction speed is reduced. Conclusively, it can be said that the introduced friction clutch model delivers comparative outcomes to a commercial musculoskeletal simulation software, while not assuming a constant tendon length. However, while presenting a relatively simple solution, an increased computation time is to be expected due to the need of a differential equation solver. Further investigation regarding implementation and computing times in more complex simulations may provide an alternative approach to conventional musculoskeletal simulations.

The objective of this thesis is to develop and demonstrate techniques for self-deployment of origami-based mechanical systems achieved through internal strain-energy storage and release, with special application to medical implant devices. The potential of compliant mechanisms and related origami-based mechanical systems to store strain-energy make them ideal candidates forapplications requiring an actuation or deployment process, such as space system arrays and minimally invasive surgical devices. The objective of this thesis is achieved by first categorizing differentdeployment methods in origami-based, deployable mechanisms and then further exploring the use of strain energy to facilitate actuation in deployable mechanisms. With this understanding inplace, there are opportunities using strain energy to develop new approaches to deploy particular mechanical systems. These origami-based mechanisms have the ability to improve devices in themedical field. This work contributes to the knowledge base of self actuating deployable structures in origami-based mechanical systems by developing design concepts and models for strain energystorage and release. By developing the foundational characteristics for self-actuation, the work will be demonstrated thorough applications in medical implant devices.

In this study, the teeth of the Carcharodon carcharias (Great White) and the Galeocerdo cuvier (Tiger) sharks were analyzed to examine their optimized structure-property relationships and edge serrations with regards to shearing. Structure-property analysis was conducted using scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy, X-ray diffraction, and optical microscopy to study the teeth using parametric optimization. Quantifying the structural properties also focused on the tooth serrations, which were captured in SEM and micrographs and were analyzed for geometric parameters using ImageJ software. Nanoindentation was performed to determine the material's mechanical properties. Further, finite element analysis (FEA) of the sharks' teeth serrations were carried out to quantify the optimum shearing performance of each serration type – zeroth (no serrations), first (a single array of serrations), and second (a secondary array of serrations upon the first array) order serration. Here, serration order, bite velocity, and angle-of-impact for ascertaining sharks' teeth shearing performance were analyzed. FEA results showed that serrated edges reduced the energy required to pierce and shear materials as the angle of penetration moved away from perpendicular to the surface. These bioinspired findings will help advance the design and optimization of engineered cutting tools.

The ability to predict the reduction in capacity of a structure after an earthquake is vital in the process of assessing a structure after a main-shock or an after-shock. Main-shocks are normally followed by a few aftershocks in a short period of time. Researchers in the past have focused for the most part on the effects of main-shocks on buildings. Very little research has been performed on the ability to predict the reduction in capacity of bridges in aftershocks. This thesis focuses on providing a way of assessing the reduction in capacity for main-shocks as compared to aftershocks and the effects and importance of both in a bridge. The reduction in capacity was defined using three different ratios: ultimate force, stiffness, and strain energy ratio. The ratios were computed relative to an undamaged state following both the main-shock scenario and the main-shock combined with aftershock scenario. The force, stiffness, and strain energy quantities were obtained from lateral pushover analyses along the two lateral bridge axes. Probabilistic demand models describing the loss in capacity were formulated by pairing intensity measures, based on real ground motions obtained from previous earthquakes, for the main-shock and aftershock with the capacity ratios, obtained from nonlinear dynamic time history analysis. Additionally, the reduction in capacity was conditioned on residual displacement and intensity measure in an attempt to discover the reduction in capacity ratio due to the contribution of residual displacement and therefore separate contributions from geometrical and material nonlinearities. This thesis demonstrates that the usage of strain energy ratio provides a definition of capacity that ultimately provides the best correlation between capacity and intensity measure.

This thesis addresses a number of challenges designers face when designing deployable origami-based arrays, specifically joint selection, design, and placement within an array. In deployable systems, the selection and arrangement of joint types is key to how the system functions. The kinematics and performance of an array is directly affected by joint performance. This work develops joint metrics which are then used to compare joint performances, constructing a tool designers can use when selecting joints for an origami array. While often a single type of joint is used throughout an array, this work shows how using multiple types of joints within the same array can offer benefits for motion deployment, and array stiffening. Origami arrays are often used for their unique solutions for stowing and deploying large planar shapes. Folds, enabled through joints, within these patterns allow the arrays to fold compactly. However, it can be difficult to fully deploy arrays, particularly array designs with a high number of joints. In addition, it is a challenge to stabilize a fully deployed array from undesired re-folding. This work introduces a strain-energy storing joint that is used to deploy and stiffen foldable origami arrays, the Lenticular Lock (LentLock). Geometry of the LentLock is introduced and the deploying and stiffening performance of the joint is shown. Folds within an origami array create the constraints that link motion between panels, and can be used to create kinematic benefits, such as creating mechanisms with a single degree-of-freedom. While many fold-constraints are required to define motion, this work shows that origami-based system contain many redundant constraints. The removal of redundant joints does not affect the motion of the array nor the observed mobility, but may decrease the likelihood of binding, simplify the overall system and decrease actuation force. This work introduces a visual and iterative approach designers can use to identify redundant constraints in origami patterns, and techniques that can be used to remove the identified redundant constraints. The presented techniques are demonstrated by removing redundant constraints from prototyped origami mechanisms. As a result of this work, designers will be better able to approach and design deployable origami-based mechanisms.

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