Euler angles, Bryant angles and Euler parameters

This chapter deals with the different approaches for describing the rotational coordinates in spatial multibody systems. In this process, Euler angles and Bryant angles are briefly characterized. Particular emphasis is given to Euler parameters, which are utilized to describe the rotational coordinates in the present work. In addition, for all the types of coordinates considered in this chapter, a characterization of the transformation matrix is fully described.

Vector of coordinates, velocities and accelerations

This chapter describes the how the vector of coordinates are defined in the formulation of spatial multibody systems. For this purpose, the translational motion is described in terms of Cartesian coordinates, while rotational motion is specified using the technique of Euler parameters. This approach avoids the computational difficulties associated with the singularities in the case of using Euler angles or Bryant angles. Moreover, the formulation of the velocities vector and accelerations vector is presented and analyzed here. These two sets of vectors are defined in terms of translational and rotational coordinates.

Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

A new approach to accurate measurement of uniaxial joint angles based on a combination of accelerometers and gyroscopes.

A new method of measuring joint angle using a combination of accelerometers and gyroscopes is presented. The method proposes a minimal sensor configuration with one sensor module mounted on each segment. The model is based on estimating the acceleration of the joint center of rotation by placing a pair of virtual sensors on the adjacent segments at the center of rotation. In the proposed technique, joint angles are found without the need for integration, so absolute angles can be obtained which are free from any source of drift. The model considers anatomical aspects and is personalized for each subject prior to each measurement. The method was validated by measuring knee flexion-extension angles of eight subjects, walking at three different speeds, and comparing the results with a reference motion measurement system. The results are very close to those of the reference system presenting very small errors (rms = 1.3, mean = 0.2, SD = 1.1 deg) and excellent correlation coefficients (0.997). The algorithm is able to provide joint angles in real-time, and ready for use in gait analysis. Technically, the system is portable, easily mountable, and can be used for long term monitoring without hindrance to natural activities.

Measurement of multi-segment foot joint angles during gait using a wearable system.

Usually the measurement of multi-segment foot and ankle complex kinematics is done with stationary motion capture devices which are limited to use in a gait laboratory. This study aimed to propose and validate a wearable system to measure the foot and ankle complex joint angles during gait in daily conditions, and then to investigate its suitability for clinical evaluations. The foot and ankle complex consisted of four segments (shank, hindfoot, forefoot, and toes), with an inertial measurement unit (3D gyroscopes and 3D accelerometers) attached to each segment. The angles between the four segments were calculated in the sagittal, coronal, and transverse planes using a new algorithm combining strap-down integration and detection of low-acceleration instants. To validate the joint angles measured by the wearable system, three subjects walked on a treadmill for five minutes at three different speeds. A camera-based stationary system that used a cluster of markers on each segment was used as a reference. To test the suitability of the system for clinical evaluation, the joint angle ranges were compared between a group of 10 healthy subjects and a group of 12 patients with ankle osteoarthritis, during two 50-m walking trials where the wearable system was attached to each subject. On average, over all joints and walking speeds, the RMS differences and correlation coefficients between the angular curves obtained using the wearable system and the stationary system were 1 deg and 0.93, respectively. Moreover, this system was able to detect significant alteration of foot and ankle function between the group of patients with ankle osteoarthritis and the group of healthy subjects. In conclusion, this wearable system was accurate and suitable for clinical evaluation when used to measure the multi-segment foot and ankle complex kinematics during long-distance walks in daily life conditions.

Calibration of angles of nozzles and deposition of an axial-flow sprayer on dwarf cashew

The study aimed to determine an optimum angle for the nozzles axial-flow sprayers a deposition for better vertical distribution focused on cashew. In laboratory tests were conducted adjusting the angle of the nozzle axial-flow sprayers. The experimental design was randomized blocks in a 2x3 factorial with four replications. The treatment for this test were two settings (with and without the adjustment of the angles of the nozzles ) and tree application volumes 273, 699 and 954 L ha-¹.The study was conducted in an orchard of dwarf cashew, with eight years of age. It was concluded that the volumetric distribution profile showed better vertical distribution uniformity when the angles of the nozzles were regulated for the canopy, the adjustment of the angles of the nozzles for the canopy provided greater deposition of droplets, the increased volume of application resulted in higher depositions in the leaves of the crop.

Receipt from D. Bryant, St. Catharines for meat

Receipt from D. Bryant, St. Catharines for meat, March 30, 1887.

Receipt from D. Bryant, St. Catharines for meat

Receipt from D. Bryant, St. Catharines for meat, May 16, 1887.

Receipt from D. Bryant, St. Catharines

Receipt from D. Bryant, St. Catharines for meat, June 14, 1887.

Receipt from D. Bryant, St. Catharines for meat

Receipt from D. Bryant, St. Catharines for meat, July 16, 1887.

Receipt from D. Bryant, St. Catharines

Receipt from D. Bryant, St. Catharines for meat, July 29, 1887

Receipt from D. Bryant, St. Catharines for meat

Receipt from D. Bryant, St. Catharines for meat, Oct. 18, 1887.