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