Design and motion control of a 6-UPS fully parallel robot for long bone fracture reduction : a thesis presented in partial fulfillment of the requirements for the degree of Master of Engineering in Mechatronics at Massey University

The incidences of long bone fractures in New Zealand are approximately 1 in 10,000. Long bones such as tibia and femur have complicated anatomic structures, making the realignment of these long bone fractures reliant on the skill of the surgeon. The drawbacks of current practice result in long time exposure to radiation, slow recovery and possible morbidity. A semi-automated long bone fracture reduction system based on a 6-DOF parallel robot platform has been in development since 2004. The developed 6-DOF parallel robot platform comprises of six linear actuators with rotary incremental encoders. To implement a realignment of long bone fractures, a framework for the 6-DOF platform robot has been developed. The inverse kinematics and singularity of the 6-DOF parallel robot has been studied to obtain the actions and Jacobin matrices. In motion control a multiple axis motion controller and amplifiers were used for 6-DOF parallel robot. PID tuning algorithms were developed based on the combination of the general tuning result and the contour control principle. The PID parameters have been validated by a number of experiments. The practical realignment of bone fractures requires a "Pull-Rotate-Push" action implemented by the 6-DOF parallel robot. After calibration, the reduction trajectories were generated accurately. The actual trials on the artificial fractures have shown that the robot developed is capable of performing the required reduction motion

Fractal properties of the random string processes

Let $\{u_t(x),t\ge 0, x\in {\mathbb{R}}\}$ be a random string taking values in ${\mathbb{R}}^d$, specified by the following stochastic partial differential equation [Funaki (1983)]: $$\frac{\partial u_t(x)}{\partial t}=\frac{{\partial}^2u_t(x)}{\partial x^2}+\dot{W},$$ where $\dot{W}(x,t)$ is an ${\mathbb{R}}^d$-valued space-time white noise. Mueller and Tribe (2002) have proved necessary and sufficient conditions for the ${\mathbb{R}}^d$-valued process $\{u_t(x):t\ge 0, x\in {\mathbb{R}}\}$ to hit points and to have double points. In this paper, we continue their research by determining the Hausdorff and packing dimensions of the level sets and the sets of double times of the random string process $\{u_t(x):t\ge 0, x\in {\mathbb{R}}\}$. We also consider the Hausdorff and packing dimensions of the range and graph of the string.Comment: Published at http://dx.doi.org/10.1214/074921706000000806 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Local times of multifractional Brownian sheets

Denote by $H(t)=(H_1(t),...,H_N(t))$ a function in $t\in{\mathbb{R}}_+^N$ with values in $(0,1)^N$. Let $\{B^{H(t)}(t)\}=\{B^{H(t)}(t),t\in{\mathbb{R}}^N_+\}$ be an $(N,d)$-multifractional Brownian sheet (mfBs) with Hurst functional $H(t)$. Under some regularity conditions on the function $H(t)$, we prove the existence, joint continuity and the H\"{o}lder regularity of the local times of $\{B^{H(t)}(t)\}$. We also determine the Hausdorff dimensions of the level sets of $\{B^{H(t)}(t)\}$. Our results extend the corresponding results for fractional Brownian sheets and multifractional Brownian motion to multifractional Brownian sheets.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ126 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Joint continuity of the local times of fractional Brownian sheets

Let $B^H=\{B^H(t),t\in{{\mathbb{R}}_+^N}\}$ be an $(N,d)$-fractional Brownian sheet with index $H=(H_1,...,H_N)\in(0,1)^N$ defined by $B^H(t)=(B^H_1(t),...,B^H_d(t)) (t\in {\mathbb{R}}_+^N),$ where $B^H_1,...,B^H_d$ are independent copies of a real-valued fractional Brownian sheet $B_0^H$. We prove that if $d<\sum_{\ell=1}^NH_{\ell}^{-1}$, then the local times of $B^H$ are jointly continuous. This verifies a conjecture of Xiao and Zhang (Probab. Theory Related Fields 124 (2002)). We also establish sharp local and global H\"{o}lder conditions for the local times of $B^H$. These results are applied to study analytic and geometric properties of the sample paths of $B^H$.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP131 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org

Removal of phenol derivatives from aqueous solution by horseradish peroxidase in the presence of additives.

It has been observed that horseradish peroxidase (HRP) can be used to remove phenol and its derivatives from wastewater. However, the large amount of HRP needed has limited its practical application. It has been reported recently that additives like polyethylene glycol (PEG) and gelatin can greatly reduce the amount of enzyme required for polymerization of phenolic compounds in high concentrations. Experiments were carried out to investigate the effect of additives on the HRP catalyzed removal of phenol derivatives at lower concentrations. Phenol derivatives studied included chlorinated phenols and methyl phenols. The results showed that there was a wide pH range, usually 6 to 8, for optimal removal of phenol derivatives. The optimum pH is mostly neutral except for 2-chlorophenol which had optimum pH of 5. Polyethylene glycol can reduce the amount of HRP needed for 95 percent or more removal of phenol derivatives from 1/30 to 1/130 and consequently, the turnovers were increased 30 to 130 times. The minimum PEG dose at a phenolic concentration of 1 mM (about 100 mg/L) varied from 30 to 100 mg/L, depending on the nature of phenolic compound. Extra PEG did not improve its effect. The time needed for the completion of polymerization varied from 1 to 3 hours at the minimum HRP and minimum PEG dose condition. For most of the phenol derivatives investigated, the optimum molar ratio of hydrogen peroxide to phenol derivatives was around 1. Coprecipitation can occur after adding additive.Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1993 .W995. Source: Masters Abstracts International, Volume: 32-02, page: 0714. Adviser: J. K. Bewtra. Thesis (M.A.Sc.)--University of Windsor (Canada), 1993

From Elasticity to Hypoplasticity: Dynamics of Granular Solids

"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well with models from soil mechanics