This dissertation presents a kinematic synthesis method developed to achieve a mechanical system that guides a natural ankle trajectory for a human walking gait. This methodology was the result of exploring hybrid task position optimization for a Watt I six-bar linkage, optimization of a four-bar linkage for 9 point path synthesis, and finally a homotopy directed optimization for a Stephenson III six-bar path generator. The new homotopy directed optimization technique was applied to 205 data points that defined the human ankle trajectory. The data was interpolated using B-splines, and an objective function, obtained from the six-bar linkage loop equations, evaluated the distance between the desired trajectory and the linkage trajectory. The result was 148 designs for 23 trajectories. A clustering algorithm was used to show that these designs are effectively the same. A complete solid model, together with a cam mechanism to control the foot orientation angle is presented. This resulted in both a new six-bar linkage synthesis methodology, as well as a unique linkage system to support natural movement of the human lower limb. The similarity of the linkage designs was exploited to introduce an adjustment that allows changes of the ankle trajectory over its natural variation.

This thesis replaces the hinged pivots of an eight-bar linkage with flexure joints in order to achieve a flexure-connected linkage system that guides rectilinear movement of its end-effector. The goal is a linkage design that can be reduced in size to provide a suspension for the proof masses of a MEMS gyroscope. The symmetric design of the linkage and its long travel relative to other MEMS suspensions has the potential to provide a number of advantages, such as the reduction of quadrature error. The design presented yields 0.1\% deviation over its range of movement. An example also presents the driving linkage of the MEMS gyroscope, which is also designed as flexure connected linkage.

Major Depressive Disorder (MDD) is a neuropsychiatric disorder characterized by persistent episodes of depressed mood and loss of interest or pleasure in normal activities. MDD patients have disturbed patterns of mood, sleep, metabolism, all factors of which are linked to circadian rhythms. The connection between MDD and abnormalities in the circadian clock has been investigated through studies on human behavior, post-mortem human brains, and animal models. We hypothesize that the abnormalities in the circadian clock persist at the molecular level, and that we can model circadian rhythms in neurons associated with MDD using induced pluripotent stem cells (iPSCs).The MDD cell line donors in this study were categorized into two groups by antidepressant response: remitters (responders) and non-remitters (non-responders) (Mrazek et al., 2014). Primary patient fibroblasts were reprogrammed into iPSCs (Vadodaria et al., 2019), which were differentiated into glutamatergic neurons, a cell type previously implicated in MDD. To measure circadian oscillatory activity, neurons were transfected with a lentivirus to deliver Per2 promoter-activated lentiviral luciferase, and bioluminescence was recorded over 5+ days. We found that MDD non-remitters neurons had lower amplitude circadian rhythms. To better understand the potential mechanisms underlying this finding, we performed qRT-PCR gene expression analysis of nine core clock genes. We found that neurons from MDD SSRI non-remitters exhibited decreased gene expression of four core circadian clock genes, PER2, PER1, CRY2, and CLOCK. These findings suggest that MDD non-remitters have a weaker circadian clock at the transcriptional level. To understand the circadian clock in MDD at the protein level, we performed immunocytochemistry of PER2 and BMAL1. MDD remitter neurons had an elevated signal of PER2 and BMAL1. Together, we demonstrate abnormalities in the molecular clock that are specific to either MDD non-remitters or remitters.

This dissertation develops a mechanism design procedures to draw algebraic plane curves. In 1876, Alfred B. Kempe published a proof that showed how to construct a linkage system obtained from the equation of an algebraic curve that draws the curve. He admitted that his approach lead to complex devices and recommended further study to achieve practical designs. Kempe's result, now called the Kempe Universality Theorem, was proven with modern mathematical precision by John Milson and Michael Kapovich in 2000. The resulting designs remain complex due to the generality of the proof. In this dissertation the focus is on the design of practical linkage systems that draw algebraic curves, trigonometric curves and Bezier curves. We also explore the realization of these linkage systems using solid models and additive manufacturing.

Bipolar disorder (BD) is a neuropsychiatric disorder that causes depressive and manic mood episodes and greatly increases the risk of suicide. People affected by BD are known to possess circadian rhythm abnormalities, and while it has been suggested that these alterations in circadian rhythms are correlated to the symptomatic mood episodes, it is unknown how these disruptions are caused or how they specifically relate to the pathogenesis of BD. To investigate the molecular mechanisms of circadian rhythms in BD, we analyzed the circadian gene expression patterns in induced pluripotent stem cell (iPSC)-derived neural progenitor cells (NPCs) and neurons from BD subjects compared to healthy subjects. Gene expression was measured across a 24-hour cycle by performing qRT-PCR on the core clock genes that control the transcriptional-translational negative feedback loop (TTFL). Expression of two clock genes in particular, CRY1 and PER2, was found to be highly expressed in BD NPCs compared to control NPCs, demonstrating that disruption of the clock may begin early on in neuronal development. Further gene expression analyses of differentiated neurons revealed that this CRY1 and PER2 finding was consistent across cell types. No other clock genes were found to have expression differences in either cell types, demonstrating some degree of specificity regarding CRY1 and PER2’s association with BD. Our analysis shows that looking into the mechanisms of circadian gene regulation in BD is a promising area of study in uncovering the molecular workings and developmental manifestation of BD.

Bipolar Disorder (BD) is a lifelong mental disorder characterized by recurrent episodes of mania and depression. Manic episodes involve elevated mood and reduced need for sleep, while depressive episodes are associated with low energy, increased/decreased sleep, and anhedonia. As such, clinical studies have shown that BD patients experience disturbed circadian rhythms. BD is heritable, as is clinical response to the first-line mood stabilizer lithium, suggesting that a biological approach to the etiology of the disorder may provide insight to BD diagnosis and treatment. Previous research in BD patient-derived fibroblasts indicates that circadian rhythm disturbances extend to the molecular level, but the relationship between BD and the cell-autonomous molecular circadian clock remains to be clarified in the most disease-relevant cell type, neurons.

Using human induced pluripotent stem cell (hiPSC)-derived neural progenitor cells (NPCs) and cortex-like glutamatergic neurons, we measured the oscillatory activity of the molecular circadian clock using a lentiviral Period2-luciferase (Per2-luc) reporter. We found that BD-associated dysregulation of the molecular clock affects NPCs. In differentiated neurons, BD Li Non-Responder (Li-NR)-derived cells were found to have circadian rhythms not modulated by lithium treatment, and were more phase-dispersed and more resistant to external entrainment factors than were BD Li Responder (Li-R) and healthy control cells. We developed a temperature-entrainment protocol that successfully induced high-amplitude, 24-hour circadian rhythms in neurons from all diagnosis groups, reversing the low-amplitude phenotype in Li-NR neurons. Further characterization of the molecular circadian rhythms of BD hiPSC-derived neurons has the potential to reveal clinically-relevant indicators of BD lithium response.

Bipolar disorder (BD) is a psychiatric disorder characterized by recurrent periods of depression and mania, accompanied by major disruptions in activity and sleep patterns. The circadian clock controls these behavioral rhythms however; genome-wide association studies have failed to identify any of the essential “clock genes” that regulate rhythms as major genetic contributors in BD, but have associated the genes encoding L-type calcium channels (LTCCs) as important risk factors. CACNA1C encodes CaV1.2, a LTCC essential for entrainment of the circadian clock. In post mortem brain studies, those with BD risk-associated variants in CACNA1C show alterations in gene expression. However, it is not known if abnormal expression of calcium channels mediates the circadian disruptions observed in BD patients. We utilized a viral per2::luciferase reporter to measure circadian rhythms in vitro and evaluate the role of a BD-associated risk allele in CACNA1C (rs4765913) and its role in human fibroblasts during phase-shifting. We found that antagonizing ryanodine receptors lengthens period whereas, blocking LTCCs shortens of the rhythm of per2::luc expression in mouse fibroblasts. Interestingly, the period changing effects of calcium channel blockers were insignificant when applied in conjunction with a temperature cycle. CACNA1C genotype (rs4765913) predicted the ability of human fibroblasts from BD patients to entrain to temperature cycles. These findings give insight as to the role of CACNA1C genotype in the ability of fibroblasts to entrain to daily stimuli, and how the abnormal entrainment displayed in BD-associated risk allele carriers could contribute to the circadian abnormalities observed in BD patients.