MECHANICS 329 FIG. 42. head to length of wedge. It is, however, difficult to estimate the power of percus- sion. To make the instrument effectual, con- siderable friction is required to prevent the resistance from forcing the wedge out of the crevice into which it has been driven. 6. The Screw. This machine is another form of the inclined plane. If a triangular piece of paper is wound around a cylinder, as shown in fig. 42, it will illustrate the formation and princi- ple of action of the screw. In passing once around the cylinder, the height be- tween two adjacent layers of the edge which forms the hypothenuse will rep- resent the height of a plane which has the circumfer- ence of the cylinder for its base. The power is applied by means of a lever, and in a direction at right angles to the axis of the screw, or in a direc- tion parallel with the base of the plane. There- fore the forces are in equilibrium where the proportion of power to resistance equals that of the distance between the threads to the cir- cumference of a circle described by the revolu- tion of that point in the lever to which the power is applied. The distance between the threads is measured in the direction of the axis of the cylinder. The power of the screw is increased by increasing the length of the lever by which it is turned, or by diminishing the distance between the threads. It may also be increased by letting a screw with compara- tively fine threads pass within another having coarser threads, thus causing the height of the plane to be practically diminished to the dif- ference in distance between the threads. This form is called Hunter's differential screw. An endless screw is often combined with spur or crown wheels in the manner shown in fig. 43. It is often employed to measure minute spaces, as in the dividing en- gine for graduating mathematical instru- ments. (See GKADTTA- TION.) Toggle Joint. The toggle joint, or elbow joint, which is used in various kinds of presses, con- sists of two radii or arms joined together by a hinge, as shown in fig. 44. The power may be applied at the hinge or joint a, usually in the direction a m, forcing the ends 5 and c further apart, and with great power as the arms approach a right line. It may also be applied at 5 and e, drawing the ends together, and forcing the point a outward in a trans- verse direction ; a form used in hay and cotton presses. That this machine acts upon the principle of the inclined plane may be demon- strated as follows : Consider the end 5 of the FIG. 43. FIG. 44. radius a I to be stationary. The power being applied in the direction a m, the point a will describe the arc of a circle ad. A tangent to this arc, at any point in which the joint a may be moving, will repre- sent the inclination, and m n the height of the plane by which the equi- librium of forces is de- termined. If the ra- dius a 5 is inclined at an angle of 45, then the inclination of the plane will be 45 ; so that if we consider it to have extension, its base will be equal to its height, and the power being ap- plied in a horizontal di- rection it will produce equilibrium when it is opposed to a force hav- ing the effect of an equivalent weight sus- pended vertically from a. As the point a ap- proaches d the tangent will approach a hori- zontal direction, and at last become perpendicular to the radii al,ac, which will then be brought to form one and the same straight line, the theoretical force at this instant becoming infinite. The ratio of power to resistance in the case represented in the figure is as mn : am, or as the height of the plane is to its base ; or p > : w : : sec I cos 5 : sin b. A carriage wheel in overcom- ing an obstacle acts upon the same principle. Let c, fig. 45, be an obstacle, and a g the line of draught. The weight, sustained by the axle at a, acts perpendicularly, and to over- come the obstacle this point must be raised to the position of Z, vertically above it. At first the motion of the axle will tend in the direction of the tangent ad, and there will be equilibrium when p : w : : dg : ag. It will successive- ly move in the direction of tan- gents at every point in the arc a 5, until it will finally take the direction of the horizontal tangent/ 5, when the obstacle will be overcome. This action has also been explained upon the principle of the lever of the first kind. The obstacle is considered as a fulcrum supporting the bent lever a c n, the arm to which the power is applied at the axle being the radius of the wheel, a c, and the other arm, c n, the horizontal distance from the obstacle to a vertical let fall from a. The
FIG. 45.
