Numerical implementation of the exact dynamics of free rigid bodies

In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on initial conditions is explicit and the equations governing the orientation of the body involve only real numbers. Based on these results, an efficient method to calculate the location and orientation of the rigid body at arbitrary times is presented. This implementation can be used to verify the accuracy of numerical integration schemes for rigid bodies, to serve as a building block for event-driven discontinuous molecular dynamics simulations of general rigid bodies, and for constructing symplectic integrators for rigid body dynamics.Comment: Shortened paper with updated references, 28 pages, 3 figure

Advancing Applications of IMUs in Sports Training and Biomechanics.

Miniature inertial measurement units (IMUs) have become popular in the field of biomechanics as an alternative to expensive and cumbersome video-based motion capture (MOCAP). IMUs provide three-axis sensing of angular velocity and linear acceleration in lieu of position data provided by MOCAP. The research presented herein further explores the use of IMUs in five applications for sports training and clinical biomechanics. The first study focuses on the sports of baseball and softball and yields estimates of the release velocity of a pitched ball within 4.6% of MOCAP measurements. The ball angular velocity further distinguishes and quantifies different types of pitches. The second study enables estimates of angular velocity during free-flight based solely on data from an embedded tri-axial accelerometer. Doing so eliminates angular rate gyros, which are often range limited, yet yields angular velocity estimates accurate to within 2%. We further exploit this technique to reveal the rotational stability of rigid bodies in free-flight. The third study extends the use of IMUs to assess the speed of an athlete estimated from a torso-mounted IMU. The speed estimates remain highly correlated with those obtained by MOCAP (r=0.96, slope=0.99) for motions characteristic of explosive sports (e.g., basketball). Moreover, the accurate speed estimation algorithm (mean RMSE=0.35 m/s) does not require data from GPS or magnetometers rendering it valuable and usable in any environment (indoor or outdoor). The remaining studies advance the use of IMU arrays to estimate joint reactions in multibody systems. The fourth study establishes the accuracy of this method using experiments on an instrumented double pendulum. Estimated reaction forces and moments remain within 5.0% and 5.9% RMS respectively of values measured via load cells. The final study addresses the companion need to measure the location of joint centers. A method employing a single IMU yields the center of rotation (CoR) of a spherical joint to within 3 mm as established by a coordinate measuring machine. The simplicity and accuracy of this method may render it attractive for broad use in field, laboratory or clinical applications requiring non-invasive, rapid estimates of joint CoR.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/97947/1/ryanmcg_1.pd

Basic set of behaviours for programming assembly robots

We know from the well established Church-Turing thesis that any computer program­ming language needs just a limited set of commands in order to perform any computable process. However, programming in these terms is so very inconvenient that a larger set of machine codes need to be introduced and on top of these higher programming languages are erected.In Assembly Robotics we could theoretically formulate any assembly task, in terms of moves. Nevertheless, it is as tedious and error prone to program assemblies at this low level as it would be to program a computer by using just Turing Machine commands.An interesting survey carried out in the beginning of the nineties showed that the most common assembly operations in manufacturing industry cluster in just seven classes. Since the research conducted in this thesis is developed within the behaviour-based assembly paradigm which views every assembly task as the external manifestation of the execution of a behavioural module, we wonder whether there exists a limited and ergonomical set of elementary modules with which to program at least 80% of the most common operations.IIn order to investigate such a problem, we set a project in which, taking into account the statistics of the aforementioned survey, we analyze the experimental behavioural decomposition of three significant assembly tasks (two similar benchmarks, the STRASS assembly, and a family of torches). From these three we establish a basic set of such modules.The three test assemblies with which we ran the experiments can not possibly exhaust ah the manufacturing assembly tasks occurring in industry, nor can the results gathered or the speculations made represent a theoretical proof of the existence of the basic set. They simply show that it is possible to formulate different assembly tasks in terms of a small set of about 10 modules, which may be regarded as an embryo of a basic set of elementary modules.Comparing this set with Kondoleon’s tasks and with Balch’s general-purpose robot routines, we observed that ours was general enough to represent 80% of the most com­mon manufacturing assembly tasks and ergonomical enough to be easily used by human operators or automatic planners. A final discussion shows that it would be possible to base an assembly programming language on this kind of set of basic behavioural modules