Will Robertson

A multipole array magnetic spring

This paper presents research on a magnetic spring concept, which has application to the development of a vibration isolation table. Features of the design are scalable, noncontact load bearing and a single degree of instability.

A Simplified Force Equation for Coaxial Cylindrical Magnets and Thin Coils

A recently-published equation for calculating the force between coaxial cylindrical magnets is presented in simplified form. The revised equation is now very compact: it is defined with fewer parameters and contains fewer terms than the original equation. The new equation is purely real, unlike the original which contained imaginary components. As a result of the simplifications, the new equation is demonstrably faster to evaluate than the original, improving its utility for parametric optimization. A reference implementation is provided for Matlab and Mathematica.

Axial Force Between a Thick Coil and a Cylindrical Permanent Magnet: Optimizing the Geometry of an Electromagnetic Actuator

In this paper, a variety of analytical/integral methods are compared for calculating the axial force between a cylindrical magnet and a “thick” solenoid that consists of many turns both radially and axially. Two newly developed techniques are introduced: one being numerical integration-based and the other completely analytical. These are compared to two other techniques, each shown to have various advantages in different contexts. One method in particular is introduced that is shown to be the most computationally efficient in the majority of actuator designs. This method is then used to optimize a typical “sleeve-type” magnet-coil actuator based on the cost function of peak force, and it is shown that optimal values of wire thickness and magnet-coil geometry can be chosen based on desired coil impedance and magnet volume.

Parameters for Optimizing the Forces Between Linear Multipole Magnet Arrays

Multipole magnet arrays have the potential to achieve greater forces than homogeneous magnets for linear spring applications. This letter investigates the effects of varying key parameters of linear multipole magnet arrays in relation to their force-bearing potential. Equal sized arrays in repulsive configurations are vertically displaced to each other; only vertical forces are compared. The force versus displacement characteristic is dependent on the aspect ratio of the arrays, the wavelength of magnetization, and the total number of magnets used in the array. Some general design guidelines for optimizing the repulsive forces are established based on the results.

Maximizing the Force Between Two Cuboid Magnets

Recently, we wrote that to maximize the force between two magnets of fixed volume, the magnet dimensions should be chosen to be as thin as possible in the direction of magnetization. This was incorrect, and we clarify this point.

Overground-Propulsion Kinematics and Acceleration in Elite Wheelchair Rugby

PURPOSE Maximal acceleration from standstill has been identified as a key performance indicator in wheelchair rugby; however, the impact of classification and kinematic variables on performance has received limited attention. This study aimed to investigate kinematic variables during maximal acceleration, with level of activity limitation accounted for using sport-classification scores. METHODS Based on their sporting classification scores, which reflect combined trunk, arm, and hand function, 25 elite wheelchair rugby players were analyzed in high-, mid-, and low-point groups before completing five 5-m sprints from a stationary position. Inertial measurement units and video analysis were used to monitor key kinematic variables. RESULTS Significant differences in kinematic variables were evident across the classification groups, particularly for the first stroke-contact angle (1-way ANOVA F2,122 = 51.5, P < .05) and first stroke time (F2,124 = 18.3, P < .05). High-point players used a first stroke-contact angle that was closer to top dead center of the wheel than either other group, while also using a shorter overall stroke time than low-point players. A linear mixed-effects model was used to investigate how kinematic variables influenced performance, with results suggesting that increased release angles (ie, farther around the wheel) and decreased stroke angles resulted in larger peak accelerations. Further investigation revealed that these results are likely influenced by strong relationships for the high-point group, as there was often no clear trend evident for midpoint and low-point groups. CONCLUSION Findings show that various propulsion approaches exist across classification groups, with this information potentially informing individual wheelchair setups and training programs.

A Halbach array magnetic spring

This paper summarises a research on a large load bearing magnetic spring concept, which has application to the development of a non-contact vibration isolation table. Also, the paper outlines the design of a magnetic spring with a single degree of instability that is suitable for bearing large loads. Analytical methods have been used to verify the stability and demonstrate the load bearing ability of the spring. Testing of the proposed magnetic spring in a physical system is currently in progress.