Robotics Class – Lesson 3 – Simple Machines Part 3 – Wedge and Screw (Compiled mostly from Wikipedia entries)
– Simple Machines –
A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refers to the six classical simple machines which were defined by Renaissance scientists:
Wheel and axle
A simple machine uses a single applied force to do work against a single load force. Ignoring friction losses, the work done on the load is equal to the work done by the applied force. The machine can increase the amount of the output force, at the cost of a proportional decrease in the distance moved by the load. The ratio of the output to the applied force is called the mechanical advantage.
– Wedge –
A wedge is a triangular shaped tool, and is a portable inclined plane, and one of the six classical simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular (normal) to its inclined surfaces. The mechanical advantage of a wedge is given by the ratio of the length of its slope to its width. Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle.
Perhaps the first example of a wedge is the hand axe. Wedges have been around for thousands of years, they were first made of simple stone. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint.
The origin of the wedge is not known. In ancient Egyptian quarries, bronze wedges were used to break away blocks of stone used in construction. Wooden wedges that swelled after being saturated with water, were also used. Some indigenous peoples of the Americas used antler wedges for splitting and working wood to make canoes, dwellings and other objects.
The blade is a compound inclined plane, consisting of two inclined planes placed so that the planes meet at one edge. When the edge where the two planes meet is pushed into a solid or fluid substance it overcomes the resistance of materials to separate by transferring the force exerted against the material into two opposing forces normal to the faces of the blade.
The blade’s first known use by humans was the sharp edge of a flint stone that was used to cleave or split animal tissue, e.g. cutting meat. The use of iron or other metals led to the development of knives for those kind of tasks. The blade of the knife allowed humans to cut meat, fibers, and other plant and animal materials with much less force than it would take to tear them apart by simply pulling with their hands. Other examples are plows, which separate soil particles, scissors which separate fabric, axes which separate wood fibers, and chisels and planes which separate wood.
Wedges, saws and chisels can separate thick and hard materials, such as wood, solid stone and hard metals and they do so with much less force, waste of material, and with more precision, than crushing, which is the application of the same force over a wider area of the material to be separated.
Other examples of wedges are found in drill bits, which produce circular holes in solids. The two edges of a drill bit are sharpened, at opposing angles, into a point and that edge is wound around the shaft of the drill bit. When the drill bit spins on its axis of rotation, the wedges are forced into the material to be separated. The resulting cut in the material is in the direction of rotation of the drill bit while the helical shape of a bit allows the removal of the cut material.
Wedges can also be used to hold objects in place, such as engine parts (poppet valves), bicycle parts (stems and eccentric bottom brackets), and doors. A wedge-type door stop (door wedge) functions largely because of the friction generated between the bottom of the door and the wedge, and the wedge and the floor (or other surface).
– Screw –
A screw is a mechanism that converts rotational motion to linear motion, and a torque (rotational force) to a linear force. The most common form consists of a cylindrical shaft with helical grooves or ridges called threads around the outside. The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw’s threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating a wood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as a nut can rotate around a stationary screw shaft. Geometrically, a screw can be viewed as a narrow inclined plane wrapped around a cylinder.
Like the other simple machines a screw can amplify force; a small rotational force (torque) on the shaft can exert a large axial force on a load. The smaller the pitch, the distance between the screw’s threads, the greater the mechanical advantage, the ratio of output to input force. Screws are widely used in threaded fasteners to hold objects together, and in devices such as screw tops for containers, vises, screw jacks and screw presses.
Other mechanisms that use the same principle, also called screws, don’t necessarily have a shaft or threads. For example, a corkscrew is a helix-shaped rod with a sharp point, and an Archimedes’ screw is a water pump that uses a rotating helical chamber to move water uphill. The common principle of all screws is that a rotating helix can cause linear motion.
Lead and Pitch –
The fineness or coarseness of a screw’s threads are defined by two closely related quantities:
— The lead is defined as the axial distance (parallel to the screw’s axis) the screw travels in one complete revolution (360°) of the
shaft. The lead determines the mechanical advantage of the screw; the smaller the lead, the higher the mechanical advantage.
— The pitch is defined as the axial distance between the crests of adjacent threads.
In most screws, called “single start” screws, which have a single helical thread wrapped around them, the lead and pitch are equal. They only differ in “multiple start” screws, which have several intertwined threads. In these screws the lead is equal to the pitch multiplied by the number of starts. Multiple-start screws are used when a large linear motion for a given rotation is desired, for example in screw caps on bottles, and ball point pens.
The helix of a screw’s thread can twist in two possible directions, which is known as handedness. Most screw threads are oriented so that when seen from above, the screw shaft moves away from the viewer (the screw is tightened) when turned in a clockwise direction. This is known as a right-handed (RH) thread, because it follows the right hand grip rule: when the fingers of the right hand are curled around the shaft in the direction of rotation, the thumb will point in the direction of motion of the shaft. Threads oriented in the opposite direction are known as left-handed (LH).
By common convention, right-handedness is the default handedness for screw threads. Therefore, most threaded parts and fasteners have right-handed threads. One explanation for why right-handed threads became standard is that for a right-handed person, tightening a right-handed screw with a screwdriver is easier than tightening a left-handed screw, because it uses the stronger supinator muscle of the arm rather than the weaker pronator muscle. Since most people are right-handed, right-handed threads became standard on threaded fasteners. Left-handed screw threads are used in some machines and in these applications:
– Where the rotation of a shaft would cause a conventional right-handed nut to loosen rather than to tighten due to fretting induced precession. Examples include:
The left hand pedal on a bicycle.
The left-hand screw holding a circular saw blade or a bench grinder wheel on.
– In some devices that have threads on either end, like turnbuckles and removable pipe segments. These parts have one right-handed and
one left-handed thread, so that turning the piece tightens or loosens both threads at the same time.
– In some gas supply connections to prevent dangerous misconnections. For example in gas welding the flammable gas supply line is attached with left-handed threads, so it will not be accidentally switched with the oxygen supply, which uses right-handed threads.
– To make them useless to the public (thus discouraging theft), left-handed light bulbs are used in some railway and subway stations.
– Coffin lids are said to have been traditionally held on with left-handed screws.
Different shapes (profiles) of threads are used in screws employed for different purposes. Screw threads are standardized so that parts made by different manufacturers will mate correctly.
Types of threads –
In threaded fasteners, large amounts of friction are acceptable and usually wanted, to prevent the fastener from unscrewing. So threads used in fasteners usually have a large 60° thread angle:
(a) V thread – These are used where additional friction is needed to make sure the screw remains motionless, such as in setscrews and adjustment screws, and where the joint must be fluid tight as in threaded pipe joints.
(b) American National – This has been replaced by the almost identical Unified Thread Standard. It has the same 60° thread angle as the V thread but is stronger because of the flat root. Used in bolts, nuts, and a wide variety of fasteners.
(c) Whitworth or British Standard – Very similar British standard replaced by the Unified Thread Standard.
In machine linkages such as lead screws or jackscrews, in contrast, friction must be minimized. Therefore threads with smaller angles are used:
(d) Square thread – This is the strongest and lowest friction thread, with a 0° thread angle, and doesn’t apply bursting force to the nut. However it is difficult to fabricate, requiring a single point cutting tool due to the need to undercut the edges. It is used in high-load applications such as jackscrews and lead screws but has been mostly replaced by the Acme thread. A modified square thread with a small 5° thread angle is sometimes used instead, which is cheaper to manufacture.
(e) Acme thread – With its 30° thread angle this has higher friction than the square thread, but is easier to manufacture and can be used with a split nut to adjust for wear. It is widely used in vises, C-clamps, valves, scissor jacks and lead screws in machines like lathes.
(f) Buttress thread – This is used in high-load applications in which the load force is applied in only one direction, such as screw jacks. With a 0° angle of the bearing surface it is as efficient as the square thread but stronger and easier to manufacture.
(g) Knuckle thread – Similar to a square thread in which the corners have been rounded to protect them from damage, also giving it higher friction. In low-strength applications it can be manufactured cheaply from sheet stock by rolling. It is used in light bulbs and sockets.
A screw conveyor uses a rotating helical screw blade to move bulk materials.
Because of its self-locking property (see below) the screw is widely used in threaded fasteners to hold objects or materials together: the wood screw, sheet metal screw, stud, and bolt and nut.
The self-locking property is also key to the screw’s use in a wide range of other applications, such as the corkscrew, screw top container lid, threaded pipe joint, vise, C-clamp, and screw jack.
Screws are also used as linkages in machines to transfer power, in the worm gear, lead screw, ball screw, and roller screw. Due to their low efficiency, screw linkages are seldom used to carry high power, but are more often employed in low power, intermittent uses such as positioning actuators.
Rotating helical screw blades or chambers are used to move material in the Archimedes’ screw, auger earth drill, and screw conveyor.
The micrometer uses a precision calibrated screw for measuring lengths with great accuracy.
Robotics Class Notes – Lesson 3