Design and analysis of logarithmic spiral type sprag one-way clutch

A complete mathematical model for logarithmic spiral type sprag one-way clutch design and analysis is given.It assumes that the motion of all clutch components can be expressed by a model of epicyclic gearing.It takes advantage of Hunt-Crossley contact impact theory to calculate the contact forces between sprags and races,and it can be used for optimization of design and comparison with other types of sprag clutches.A good deal of analysis shows that the parameters of the steady windup angle,the steady contact force,the natural frequency and natural cycle of clutch have nothing to do with the initial velocity of outer race,while the parameters of the maximum transient windup angle,the maximum transient impact force and the steady engagement time increase linearly in the mode of engaging operation of clutch.It is also shown that the strut angle has great influence on the dynamic engagement performance of clutch.The parameters of the steady windup angle,the maximum transient windup angle,the steady engaging time,the steady contact force,the maximum transient impact force and the natural cycle of clutch decrease linearly nearly with the inner strut angle,while the natural frequency of the system increases linearly with the inner strut angle.

A modified logarithmic spiral method for determining passive earth pressure

In this study, a modified logarithmic spiral method is proposed to determine the passive earth pressure and failure surface of cohesionless sloping backfill, with presence of wallesoil interface friction. The proposed method is based on a limit equilibrium analysis wherein the assumed profile of the backfill failure surface is a composite of logarithmic spiral and its tangent. If the wallesoil interface is smooth, a straight line does not need to be assumed for the failure surface. The geometry of the failure surface is determined using the Mohr circle analysis of the soil. The resultant passive earth thrust is computed considering equilibrium of moments. The passive earth pressure coefficients are calculated with varied values of soil internal friction angle and cohesion, wall friction angle and inclination angle, and sloping backfill angle. This method is verified with the finite element method(FEM) by comparing the horizontal passive earth pressure and failure surface. The results agree well with other solutions, particularly with those obtained by the FEM. The implementation of the present method is efficient. The logarithmic spiral theory is rigorous and self-explanatory for the geotechnical engineer.

The Design of Form Milling Cutter as the Curve of the Back of Tooth Is Logarithmic Spiral

Form milling cutter is built-for-purpose cutter which process the form surface, for example, usually process male and female circular arc face and form trench and so on. From the traditional concept, form milling cutter is divided into pointed tooth and relieving follow its structure. Relieving shaped cutter is more convenient than pointed tooth milling cutter, because only its rake face is needed to grind after it turn into blunting, so the current books which are used in college almost select relieving shaped cutter in order to introduce how to design the form milling cutter.The curve of the back of tooth of relieving cutter is the transversal which is formed by the rear face of tooth in the end cut plane of the milling cutter. In the past, because of the limit of the manufacturing technology, the curve of the back of tooth is often selected Archimedes’ curve, in order that the shovel-nose tool acquire the uniform motion when the cutter shovel the back, in other word, the rear face of the milling cutter rotate its axis by the new cutting lip, in the same time, it move uniformly to the axis in order to form the surface. Although this curve of the back of tooth meet the fixedness of the form of blade around grinding the cutter, the rear angle of the dot of the cutting lip don’t keep fixedness. With the development of the modern manufacturing technology, the unmanageable problem of many complex curves is already easily solved. So it is need to study the optimum profile of the curve of the back of tooth in theory, and study the design theory of the relieving shaped cutter under the condition of new manufacture, in order to ensure that the rear angle of the dot of the cutting lip keep fixedness after the relieving shaped cutter is grinded. The paper derive the curve profile of tooth of the form cutter and the modifier calculation formula of the profile of the cutter edge from the definition of the rear angle of the cutter, which establish the foundation for the precision design and manufacture of other form cutter.

The Layout and Simulation of Logarithmic Spiral Double Curved Arch Dam Transverse Joints

Because of its good condition with mechanics, logarithmic spiral double curve arch bam has been widely used in the practical engineering. The introduction of a new method in how to divide transverse joint in arch dam will be given and the further research of its calculation has been done. The C＋＋ is used in electronic procedure and the 3D simulation has been finished with AutoCAD, which will provide the object model for computer simulation of the arch dam and the division of finite element mesh. Meanwhile, this method in dividing the transverse joint in arch dam also can be taken as the calculated basis for the design and calculation of arch dam, construction lofting and the calculation of the work amount.

Analytical solution to logarithmic spiral trajectories with circumferential thrust and mission applications

This study made use of a shape-based method to analyze the orbital dynamics of a spacecraft subject to a continuous propulsive acceleration acting along the circumferential direction.Under the assumption of a logarithmic spiral trajectory,an exact solution to the equations of motion exists,which allows the spacecraft state variables and flight time to be expressed as a function of the angular coordinate.There is also a case characterized by specific initial conditions in which the time evolution of the state variables may be analytically determined.In this context,the presented solution is used to analyze circle-to-circle trajectories,where the combination of two impulsive maneuvers and a logarithmic spiral path are used to accomplish the transfer.The determined results are then applied to the achievement of the Earth–Mars and the Earth–Venus transfers using actual data from a recent thruster developed by NASA.

A “logarithmic spiral” in the brain: Images of an intracranial dermoid cyst

A logarithmic spiral is a self-similar spiral curve, which often appears in nature, e.g., mollusk shells. In the normal tissues of the human body, the cochlea is also an approximate logarithmic spiral. However, approximate logarithmic spirals are rarely,if ever, reported in tumors. Recently, we treated a 26-year-old woman with a one-year history of headache. Preoperative magnetic resonance imaging showed a possible brain tumor with radiological characteristics similar to a typical logarithmic spiral,which has seldom been observed before. Because of the obvious clinical symptoms and discomfort, as well as the possible presence of an intracranial tumor, we performed a craniotomy and tumor resection. Perioperatively, we found an intact tumor capsule,with contents that appeared like egg-drop soup mixed with hairs. A post-operative pathological diagnosis of a dermoid cyst was made. However, more interestingly, the logarithmic spiral could be described mathematically with a high goodness of fit. In this paper, we present this case with various clinical images.

Spacelike Mobius Hypersurfaces in Four Dimensional Lorentzian Space Form

In this paper, we first set up an alternative fundamental theory of M?bius geometry for any umbilic-free spacelike hypersurfaces in four dimensional Lorentzian space form, and prove the hypersurfaces can be determined completely by a system consisting of a function W and a tangent frame {E_i}. Then we give a complete classification for spacelike M?bius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either M?bius equivalent to spacelike Dupin hypersurfaces or to some cylinders constructed from logarithmic curves and hyperbolic logarithmic spirals. Some of them have parallel para-Blaschke tensors with non-vanishing M?bius form.