Diaboloidal mirrors: algebraic solution and surface shape approximations

A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X-ray optics is the collimated two-crystal monochromator, with toroidal mirror refocusing. The element here replaces the toroid, and in such a system provides completely aberration free, point-to-point imaging of rays from the on-axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.

Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY

The code COSY INFINITY uses a beamline coordinate system with a Frenet–Serret frame relative to the reference particle, and calculates differential algebra-valued transfer maps by integrating the ODEs of motion in the respective vector space over a differential algebra (DA). We described and performed computation of the DA transfer map of an electrostatic spherical deflector in a laboratory coordinate system using two conventional methods: (1) by integrating the ODEs of motion using a numerical integrator and (2) by computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. We compared the resulting transfer maps with (3) the DA transfer map of COSY INFINITY’s built-in electrostatic spherical deflector element [Formula: see text] and (4) the transfer map of the electrostatic spherical deflector computed using the program GIOS, which uses analytic formulas from a paper1 by Hermann Wollnik regarding second-order aberrations. In addition to the electrostatic spherical deflector, we studied an electrostatic cylindrical deflector, where the Kepler theory is not applicable. We computed the DA transfer map by the ODE integration method (1), and we compared it with the transfer maps by (3) COSY INFINITY’s built-in electrostatic cylindrical deflector element [Formula: see text] and (4) GIOS. The transfer maps of electrostatic spherical and cylindrical deflectors obtained using the direct calculation methods (1) and (2) are in excellent agreement with those computed using (3) COSY INFINITY. On the other hand, we found a significant discrepancy with (4) the program GIOS.

Strain Gauged Six-Component Load Transducer for use in Upper Limb Biomechanics

A six-channel instrumented load transducer has been developed for measuring hand and upper limb loading (maximum design load, 2 kN). Modular in design, the transducer can be adapted to a variety of formats, thereby increasing the range of activities to which it can be applied. When used with a motion analysis system, hand loading can be determined with respect to a laboratory coordinate system irrespective of transducer orientation and position. Measurement accuracy of approximately ± 1 per cent of applied loading has been determined through a system calibration.

Differences in Ankle Joint Complex Range of Motion as a Function of Age

The purpose of this study was to determine whether gender- and age-related differences in ankle joint complex (AJC) range of motion (ROM) exist in children (range 9–13 years), adolescents (14–16 years), and young adults (17–20 years), and to compare these data with those published for older subjects (21–79 years) using the same protocol. 15 A total of 120 subjects (58 males and 62 females) ranging in age from 9 to 20 years were tested for AJC ROM using a specifically designed 6° of freedom fixture. 1 All measurements were made with respect to a laboratory coordinate system, and represented assessment of active AJC ROM. Angular displacements for plan-tarflexion, dorsiflexion, inversion, eversion, abduction, and adduction were digitally recorded and compared. AJC ROMs of females aged 9 to 20 years were generally greater than those for males about all three orthogonal axes. Within each gender, there was a consistent trend for AJC ROM to decrease from a maximum at 14 to 16 or 17 to 20 years to a minimum after age 60 years. The average decrement was greater for females than for males. This study provided evidence to support the contention that age-related and gender differences in AJC ROM do exist. The possibility of minimizing the decline in AJC ROM with age requires further investigation.

Range of Motion of the Foot as a Function of Age

Movement of the foot is essential for human locomotion. The purpose of this paper was to quantify the range of motion of the foot as a function of age and to compare the rage of motion measurements for the foot in a laboratory coordinate system and a coordinate system fixed to the tibia. The measurements were taken in vivo using a range of motion instrument developed by Allinger (University of Calgary, Canada, 1990) from 121 subjects. The results suggest that: (1) the range of motion in general is greater for women than for men in the young adult group; (2) the range of motion in general is in the same order of magnitude for women and men in the oldest age group; and (3) the range of motion is about 8° smaller in dorsiflexion and about 8° higher in plantarflexion for women than for men in the oldest age group. It is speculated that physical activity and common shoe wear are factors influencing the age- and gender-dependent differences in range of motion. Furthermore, it has been shown that the range of motion values measured in a laboratory coordinate system and in a coordinate system fixed in the tibia are different in all directions except inversion. The differences in plantarflexion and dorsiflexion and inversion and eversion are relatively small. However, they are substantial for adduction and abduction. In all cases, the results were bigger for measurements in the laboratory coordinate system compared with the tibia coordinate system, because the movement of the lower leg was included in the measurements in the laboratory coordinate system. The data indicate that foot range of motion is different for women and men. Consequently, it is speculated that these differences may be related to possible overloading of the locomotor system, especially in sporting activities in which the loading of the foot is significant. The differences in the plantarflexion and dorsiflexion direction were assumed to influence the loading of the Achilles tendon, and it is suggested that some of the Achilles tendon problems may be predictable based on range of motion measurements.