Word Finder - axes

definition

A tool for felling trees or chopping wood etc. consisting of a heavy head flattened to a blade on one side, and a handle attached to it.

definition

An ancient weapon consisting of a head that has one or two blades and a long handle.

definition

A dismissal or rejection.

example

His girlfriend/boss/schoolmaster gave him the axe.

synonyms

• boot
• chop
• pink slip
• sack

definition

A gigging musician's particular instrument, especially a guitar in rock music or a saxophone in jazz.

definition

A position, interest, or reason in buying and selling stock, often with ulterior motives.

example

A financial dealer has an axe in a stock that his buyers don't know about, giving him an advantage in making the most profit.

definition

The axle of a wheel.

Axes and choppers were plied all around.

The steady chinking of ice axes could be heard echoing up and down the deep gorge.

She'd thought his wall of swords, daggers, axes, and other medieval weapons were for ceremony.

Near this domestic quarter was found a small shrine of the Double Axes, with cult objects and offertory vessels in their places.

A crystal may be regarded as built up of primitive parallelepipeda, the edges of which are in the ratio of the crystallographic axes, and the angles the axial angles of the crystals.

The oldest rocks, the gneisses and schists of the Archean period, form nearly the whole of the Central Plateau, and are also exposed in the axes of the folds in Brittany.

We can distinguish (I) digestive endoderm, in the stomach, often with special glandular elements; (2) circu-, latory endoderm, in the radial and ring canals; (3) supporting endoderm in the axes of the tentacles and in the endodermlamella; the latter is primitively a double layer of cells, produced by concrescence OC-- = w.?"

The main assimilating tissue, on the other hand, is under the upper epidermis, where it is well illuminated, and consists of oblong cells densely packed with chloroplasts and with their long axes perpendicular to the surface (palisade tissue).

The rotation of the planets on their axes is also explained as a consequence of the nebular theory, for at the time of the first formation of the planet it must have participated in the rotation of the whole nebula, and by the subsequent contraction of the planet the speed with which the rotation was performed must have been accelerated.

Their weapons consisted of bow and arrows, short swords, spears and axes.

Moving Axes in Hydrodynamics.

The driving circle was greatly increased in diameter and placed at the upper end of the polar axis, and both the polar and declination axes were made much stronger in proportion to the mass of the instrument they were designed to carry.

This solution, taken by itself, represents a motion in which each particle of the system (since its displacements parallel to Cartesian co-ordinate axes are linear functions of the qs) executes a simple vibration of period 21r/u.

The pyro-electric characters of quartz are closely connected with its peculiar type of symmetry and especially with the three uniterminal dyad axes.

Take, for example, the case of a sphere rolling on a plane; and let the axes Ox, Oy be drawn through the centre parallel to the plane, so that the equation of the latter is 1=cf.

Let a be the radius of the rolling sphere, c that of the spherical surface which is the locus of its centre, and let x, y, I be the co-ordinates of this centre relative to axes through 0, the centre of the fixed sphere.

If p, q, r be the component angular velocities about the principal axes at 0, we have (Ap+B2q+C,2)/r = (Ap+Bq1+Cr2)/2T, (3) each side being in fact equal to unity.

The ratio of the axes of the ellipse is sec a, the longer axis being in the plane of 0.

Moving A xes of ReferenceFor the more general treatment of the kinetics of a rigid body it is usually convenient to adopt a system of moving axes.

In order that the moments and products of inertia with respect to these axes may be constant, it is in general necessary to suppose them fixed in the solid.

The moving axes Ox, Oy, 01 form a rigid frame of reference whose motion at time t may be specified by the three component angular velocities p, q, r.

Now consider a system of fixed axes Ox, Oy, Oz chosen so as to coincide at the instant I with the moving system Ox, Oy, Os.

If we now apply them to the case of a rigid body moving about a fixed point 0, and make Ox, Oy, Oz coincide with the principal axes of inertia at 0, we have X, u, v=Ap, Bq, Cr, whence A (B C) qr = L,

These equations are due to Euler, with whom the conception of moving axes, and the application to the problem of free rotation, originated.

When, in any problem, the values of u, v, w, p, q, r have been determined as functions of t, it still remains to connect the moving axes with some fixed frame of reference.

Let yr be the linear velocity of the point E fixed in the plane of axes AOB.

Application to a Pair of TurnIng Fseces.Let ai, a2 be the angular velocities of a pair of turning pieces; Of, Oi the angles which their line of connection makes with their respective planes of rotation; Ti, r2 the common perpendiculars let fall from the line of connection upon the respective axes of rotation of the pieces.

That, when both pieces rotate, their axes, and all their points of contact, lie in the same plane.

That the angular velocities of a pair of turning pieces in rolling contact must be inversely as the perpendicular distances of any pair of points of contact from the respective axes.

That for a pair of turning pieces with parallel axes, and for a turning piece and a shifting piece, the line of contact is straight, and parallel to the axes or axis; and hence that the rolling surfaces are either plane or cylindrical (the term cylindrical including all surfaces generated by the motion of a straight line parallel tO itself).

Cylindrical Wheels and Smooth Racks.In designing cylindrical wheels and smooth racks, and determining their comparati* motion, it is sufficient to consider a section of the pair of pieces made by a plane perpendicular to the axis or axes.

The points where axes intersect the plane of section are called centres; the point where the line of contact intersects it, the poini of contact, or pitch-point; and the wheels are described as circular, elliptical, &c., according to the forms of their sections made by that plane.

The axes will not be parallel, nor will they intersect each other.

The pitch-circles of a pair of circular toothed wheels are sections of their pitch-surfaces, made for spur-wheels (that is, for wheels whose axes are parallel) by a plane at right angles to the axes, and for bevel wheels by a sphere described about the common apex.

The ordinary position of a pair of endless screws is with their axes at right angles to each other.

Ci, C1 are the axes of the two parallel shafts; Di, D2 two disks facing each other, fixed on the ends of the two shafts FIG.

Oldhams coupling may be used with advantage where the axes of the shafts are intended to be as nearly in the same straight line as is possible, but where there is some doubt as to the practibility I or nermanency of their exact continuity.

The length L of an endless belt connecting a pair of pulleys whose effective radii are r,, r,, with parallel axes whose distance apart is c, is given by the following formulae, in each of which the first term, containing the radical, expresses the length of the straight parts of the belt, and the remainder of the formula the length of the curved parts.

That condition is / fulfilled by a pair of con- B ?-D tinuous cones generated by - \ the revolution of two straight 2 / lines inclined opposite ways to -, their respective axes at equal angles.

Let r1 be the radius of the large end of each, ri that of the small end, r, that of the middle; and let Ii be the sagitta, measured perpendicular to the axes, of the arc by whose revolution each of the conoids is generated, or, in other words, the bulging of the conoids in the middle of their length.

The effect of the link is to maintain the distance between the axes of those pins invariable; hence the common perpendicular of the axes of the pins is the line of connection, and its extremities may be called the connected points.

The axes of rotation of a pair of turning pieces connected by a link are almost always parallel, and perpendicular to the line of connection n which case the angular velocity ratio at any instant is the recipocal of the ratio of the common perpendiculars let fall from the me of connection upon the respective axes of rotation.

The velocity of the other connected point at such an instant is null, unless it also reaches a dead-point at the same instant, so that the line of connection is in the plane of the two axes of rotation, in which case the velocity ratio is indeterminate.

Coupling of Parallel Axes.Two or more parallel shafts (such as those of a locomotive engine, with two or more pairs of driving wheels) are made to rotate with constantly equal angular velocities by having equal cranks, which are maintained parallel by a coupling-rod of such a length that the line of c000exion is equal to the distance between the axes.

Let 0 be the point of intersection of the axes OCf, 0C2,

Let the axis Ai carry a wheel of N1 teeth, driving a wheel of ni teeth on the axis Ai, which carries also a wheel of N2 teeth, driving a wheel of 113 teeth on the axis A3, and so on; the numbers of teeth in drivers being denoted by Ns, and in followers by ns, and the axes to which the wheels are fixed being denoted by numbers.

Supposing all the wheels to be in outside gearing, then, as each elementary combination reverses the direction of rotation, and as the number of elementary combinations m 1 is one less than the number of axes rn it is evident that if m is odd the direction of rotation is preserved, and if even reversed.

It is often a question of importance to determine the number of teeth in a train of wheels best suited for giving a determinate velocity ratio to two axes.

It was shown by Young that, to do this with the least total number of teeth, the velocity ratio of each elementary combination should approximate as nearly as possible to 3.59., This would in many cases give too many axes; and, as a useful practical rule, it may be laid down that from 3 to 6 ought to be the limit of the velocity ratio of an elementary combination in wheelwork.

Adding the centres corresponding to these several axes to the figure, it will be seen that there are six centres in connection with the four-bar chain of which four are permanent and two are instantaneous or virtual centres; and, further, that whatever be the configuration of the chain these centres group themselves into three sets of three, each set lying on a straight line.