Systems and methods for joint replacement are provided. The systems and methods include a surgical orientation device and at least one orthopedic fixture. The surgical orientation device and orthopedic fixtures can be used to locate the orientation of an axis in the body, to adjust an orientation of a cutting plane or planes along a bony surface, to distract a joint, or to otherwise assist in an orthopedic procedure or procedures.

Systems and methods for joint replacement

Various embodiments provide systems and methods capable of facilitating interaction with handheld electronics devices based on sensing rotational rate around at least three axes and linear acceleration along at least three axes. In one aspect, a handheld electronic device includes a subsystem providing display capability, a set of motion sensors sensing rotational rate around at least three axes and linear acceleration along at least three axes, and a subsystem which, based on motion data derived from at least one of the motion sensors, is capable of facilitating interaction with the device.

Controlling and accessing content using motion processing on mobile devices

Ordinary differential equations of the first order linear differential equations complex numbers and linear algebra simultaneous linear differential equations numerical methods the descriptive theory of nonlinear differential equations mechanical systems and electric circuits Fourier series Fourier integrals and Fourier transforms the Laplace transformation partial differential equations Bessel functions and Legendre polynomials applications and further properties of matrices vector analysis the calculus of variations analytic functions of a complex variable infinite series in the complex plane the theory of residues conformal mapping.

Advanced Engineering Mathematics. By C. R. Wylie. Pp. xiv, 813. 1966. (McGraw-Hill.)

We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Our approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description---we represent the material frame by its angular deviation from the natural Bishop frame---as well as in the dynamical treatment---we treat the centerline as dynamic and the material frame as quasistatic. Additionally, we describe a manifold projection method for coupling rods to rigid-bodies and simultaneously enforcing rod inextensibility. The use of quasistatics and constraints provides an efficient treatment for stiff twisting and stretching modes; at the same time, we retain the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. We validate the discrete rod model via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons.

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Discrete elastic rods

Physical Biology of the Cell, 2nd Edition, is a textbook that focuses on the application of physical principles to understanding biological systems. The subject matter of the text is organized according to common physical principles that govern biological processes rather than in relation to the biological processes themselves, as is common for most biology and cell biology textbooks. Topics covered in the book span a broad range of interests, including electrostatics, molecular interactions, molecular motors and the cytoskeleton, and membranes. Each chapter features color figures, derived equations with relevant examples, and problem sets at the chapter’s conclusion. The problem sets at the end of the chapters are expanded from the first edition. Further, the second edition includes two new chapters, one on light and pattern formation, and another on the use of computation in exploring biological problems. Additional student and instructor resources are also available online.

The primary audience for the textbook could include advanced undergraduate students or first-year graduate students. While the textbook may be best suited for a biophysics course, it could also be used as a primary or supplementary text for teaching cellular and molecular biology. As a teaching tool for cellular and molecular biology, the many examples featured throughout the text could easily be employed to assist students in learning the principles of how a cellular or molecular system functions. A basic level of mathematical proficiency would be required of the student. While this textbook could be an excellent resource for many courses, there are several topics commonly covered in biochemistry classes, such the glycolytic pathway, that are featured in the book but in different contexts than many widely used biochemistry texts. For a biophysics course that is heavily focused on techniques, individual references that discuss the specific techniques in detail would be more suitable than this book. Of course, any instructor seeking to use this textbook should be aware of its content before making a selection.

This textbook is an excellent resource, both for a research scientist and for a teacher. The authors do a superb job of selecting the material for each chapter and explaining the material with equations and narrative in an easily digestible manner. Readers who enjoy this book may also enjoy Molecular Driving Forces by Dill and Bromberg, which gives excellent treatment of similar concepts.

Physical Biology of the Cell

A theoretical model is derived which describes the non-linear response of a suspended elastic cable to small tangential oscillations of one support. The support oscillations, in general, result in parametric excitation of out-of-plane motion and simultaneous parametric and external excitation of in-plane motion. Cubic non-linearities due to cable stretching and quadratic nonlinearities due to equilibrium cable curvature couple these motion components in producing full, three-dimensional cable response. In this study, a two-degree-of-freedom approximation of the model is employed to examine a class of in-plane/out-of-plane motions that are coupled through the quadratic non-linearities. A first-order perturbation analysis is utilized to determine the existence and stability of the planar and non-planar periodic motions that result from simultaneous parametric and external resonances. The analysis leads to a bifurcation condition governing planar stability and results highlight how planar stability is reduced and non-planar response is enhanced whenever a “two-to-one” internal resonance condition exists between a pair of in-plane and out-of-plane cable modes. This two-to-one resonant behavior is clearly observed in experimental measurements of cable response which are also in good qualitative agreement with theoretical predictions.

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Modal interactions in the non-linear response of elastic cables under parametric/external excitation

Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables

An application of rate gyros and accelerometers allows electronic measurement of the motion of a rigid or semi-rigid body, such as a body associated with sporting equipment including a fly rod during casting, a baseball bat, a tennis racquet or a golf club during swinging. For instance, data can be collected by one gyro according to the present invention is extremely useful in analyzing the motion of a fly rod during fly casting instruction, and can also be used during the research, development and design phases of fly casting equipment including fly rods and fly lines. Similarly, data collected by three gyros and three accelerometers is extremely useful in analyzing the three dimensional motion of other sporting equipment such as baseball bats, tennis racquets and golf clubs. This data can be used to support instruction as well as design of the sporting equipment.

Electronic measurement of the motion of a moving body of sports equipment

The near-resonant response of suspended, elastic cables driven by planar excitation is investigated using a two degree-of-fredom model. The model captures the interaction of a symmetric in-plane mode and an out-of-plane mode with near commensurable natural frequencies in a 2:1 ratio. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. The existence and stability of periodic solutions are investigated using a second order perturbation analysis. The first order analysis shows that suspended cables may exhibit saturation and jump phenomena. The second order analysis, however, reveals that the cubic nonlinearities and higher order corrections disrupt saturation. The stable, steady state solutions for the second order analysis compare favorably with results obtained by numerically integrating the equations of motion.

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Nonlinear oscillations of suspended cables containing a two-to-one internal resonance

The emergence of accurate MEMS inertial sensors motivates the design of miniature inertial measurement units (IMU) for applications well outside the field of inertial navigation. One promising application concerns novel sports training systems with inertial sensors embedded directly in sports equipment. This paper describes the theory, design, and evaluation of a miniature, wireless IMU that precisely measures the dynamics of a golf club used in putting. The design consists of a complete six degree-of-freedom IMU composed of MEMS accelerometers and angular rate gyros with an integrated microprocessor and RF transceiver. The resulting sensor system has negligible mass (25 g relative to 490 g for the putter) and is a mere 13 mm in diameter allowing it to fit wholly within the shaft of the club at the grip end. The measurement theory enables the computation of the position, velocity, and orientation of the club head at the opposite end of the shaft during the entire putting stroke. Experiments reveal that the three-dimensional position and orientation of the club head can be resolved to within 3 mm and 0.5°, respectively. These achievements yield a highly accurate, portable, and inexpensive sensor system to support golf swing training, custom club fitting, and club design.

Noel C. Perkins

Papers

Modal interactions in the non-linear response of elastic cables under parametric/external excitation

Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables

Electronic measurement of the motion of a moving body of sports equipment

Nonlinear oscillations of suspended cables containing a two-to-one internal resonance

Wireless MEMS inertial sensor system for golf swing dynamics