A new equilibrator design approach based on system potential energy functions is presented. This approach was used to discover a group of spring equilibrators which perfectly balance a rotatable rigid link at every orientation angle through 360 deg of link rotation. Springs are connected between a rotatable link and ground, where one end of each spring is connected to the rigid link and the other end of each spring is connected to ground. The rigid link is connected to ground by a pin joint and is free to rotate about that joint. The conditions for existence and the design equations for all equilibrators which fall into this category are developed and presented. Three designs appear to offer unique advantages over the infinite number of design options available.
This manuscript provides a mathematical basis for comparing the complexity of equilibrator methodologies, extends the applications of those methodologies, and develops new methodologies. Two methodologies exist for spring equilibration of two degree of freedom revolute joint planar linkages. Extensions of both methodologies are now demonstrated for equilibration of all rigid body planar linkages having lower and/or higher order kinematic pairs. Reduction in complexity of these general methodologies is demonstrated when kinematic chains include only revolute joints. A mathematical description of the complexity of each of three equilibration methodologies is introduced to provide a means of comparing the effectiveness of each approach. Examples demonstrate the appropriate equilibrator design choice for particular applications, based on the mathematical description of system complexity. A new approach for equilibration of linkages having higher order planar kinematic pairs (1R1T) is introduced. A solution to the problem of spring mass in equilibrator design is presented. Examples are included to demonstrate the effectiveness of both the 1R1T equilibrator design scheme, and the spring mass equilibration scheme. The 1R1T design represents a first equilibration of pantograph type mechanisms.
The goal of this study was to develop and validate a finite element model (FEM) for use in the design of a flooring system that would provide a stable walking surface during normal locomotion but would also deform elastically under higher loads, such as those resulting from falls. The new flooring system is designed to reduce the peak force on the femoral neck during a lateral fall onto the hip. The new flooring system is passive in nature and exhibits two distinct stiffnesses. During normal activities, the floor remains essentially rigid. Upon impact, the floor collapses and becomes significantly softer. The flooring system consists of a multitude of columns supporting a continuous walking surface. The columns were designed to remain stiff up to a specific load and, after exceeding this load, to deform elastically. The flooring returns to its original shape after impact. Part I of this study presented finite element and experimental results demonstrating that the floor deflection during normal walking remained less than 2 mm. To facilitate the floor's development further, a nonlinear finite element model simulating the transient-impact response of a human hip against various floor configurations was developed. Nonlinearities included in the finite element models were: changing topology of deformable-body-to-deformable-body contact, snap-through buckling, soft tissue stiffness and damping, and large deformations. Experimental models developed for validating the finite element model included an anthropomorphic hip, an impact delivery mechanism, a data collection system, and four hand-fabricated floor tiles. The finite element model discussed in this study is shown to capture experimentally observed trends in peak femoral neck force reduction as a function of flooring design parameters. This study also indicates that a floor can be designed that deflects minimally during walking and reduces the peak force on the femoral neck during a fall-related impact by 15.2 percent.
A new flooring system has been developed to reduce peak impact forces to the hips when humans fall. The new safety floor is designed to remain relatively rigid under normal walking conditions, but to deform elastically when impacted during a fall. Design objectives included minimizing peak force experienced by the femur during a fall-induced impact, while maintaining a maximum of 2 mm of floor deflection during walking. Finite Element Models (FEMs) were developed to capture the complex dynamics of impact response between two deformable bodies. Validation of the finite element models included analytical calculations of theoretical buckling column response, experimental quasi-static loading of full-scale flooring prototypes, and flooring response during walking trials. Finite Element Method results compared well with theoretical and experimental data. Both finite element and experimental data suggest that the proposed safety floor can effectively meet the design goal of 2 mm maximum deflection during walking, while effectively reducing impact forces during a fall.
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