Hiscox - 1800 Mechanical Movements, Devices and Appliances

FORCES AND THE MEASURE OF THEIR WORK.

FORCE may be said to be the cause of motion and power m mechanics. Its condition may be static or dynamic; in the latter condition it becomes the means for the practical application of motion in the various forms of mechanical devices. Its statical condition is illustrated in the strains sustained in the material of construction and suspension.

The first and simple form of static force may be illustrated in the column, in the various positions in which it may be used for resistance of any kind; although in machinery, it may in itself become a moving body under stress. Static force may be represented by a column supporting weight; a beam under compressive strain; a body of water retained in a mill dam, steam pressure in a boiler, compressed air or liquefied gases, and a suspended weight; a coiled spring or anything that is under pressure without motion. The principal expressions for static force are compression, tension, and torsion, or their combinations. The resolution of forces is the geometrical relation and value of two or more forces acting upon a single point from different directions, or of a single force acting against several points of resistance.

The terms of resolution may be directional, static, or dynamic.

3. THE RESOLUTION OF SUSPENSIONin which W represents a force or the weight of gravitation, and P, P the resisting power or equivalent weights. Solution:

when the angles are equal.

4. For unequal angles the forces vary as the sines of the angles from the vertical, respectively.

Solution:

5. In a combination of forces the resolution involves the sines of the varying angles.

6. The forces in the direction of P and P in which the weight of a beam inclined and resting upon a point at P = W, at the centre of gravity.

The longitudinal thrust of struts or braces is the same as for tensional strains inversely, only that the weight of timbers or heavy materials should be considered separately, as shown further on.

7. Where the members are of the same length and at equal angles.

8. For unequal angles.

Solution:

9. With truss beams carrying unequal weights the formulae for end thrust are for equal angles.

For unequal angles, the formula is the same as in No. 8.

10. LEVER PARADOX. Two levers or scale beams, one above the other, accurately balanced and pivoted at their ends to two T arms as shown in the cut, may have equal weights hung at various distances on the arms, and they will be balanced on the centre line and at any angle above or below the centre line. A nut for amateurs to crack.

THE LEVER AND ITS POWER.

The weight of lever is not considered.

11. First order.

12. Second order.

13. Third order.

14. Bell Crank or Angular Lever, first order. Same notation as No. 11.

15. Bell Crank or Angular Lever, second order. Same Notation as No. 12.

16. Bell Crank or Angular Lever, third order.