Harmonic Drive is the brand name of strain wave gear trademarked by the Harmonic Drive company, invented in 1957 by C. W. Musser, it is commonly implemented in robotics today and used in aerospace as well, for gear reduction but may be used to increase rotational speed, or for differential gearing. The basic concept of strain wave gearing was introduced by C. W. Musser in his 1957 patent, it was first used in 1960 by USM Co. and by Hasegawa Gear Works, Ltd. under license of USM. Hasegawa Gear Works, Ltd. became Harmonic Drive Systems Inc. located in Japan and USM Co. Harmonic Drive division became Harmonic Drive Technologies Inc; the electrically driven wheels of the Apollo Lunar Rover included strain wave gears in their gearing. The winches used on Skylab to deploy the solar panels were powered using strain wave gears. Both of these system were developed by The Harmonic Drive Division of United Shoe Machinery Corp. On January 1, 2006, Harmonic Drive Technologies/Nabtesco of Peabody, MA and HD Systems of Hauppauge, NY, merged to form a new joint venture, Harmonic Drive LLC.
HD Systems, Inc. was a subsidiary company of Inc.. Offices are maintained in Peabody, MA, Hauppauge, NY, San Jose, CA and Oak Park, IL. Harmonic Drive Systems, Inc. Japan is headquartered in Tokyo with its primary manufacturing location in Hotaka, Japan. Harmonic Drive AG has its European manufacturing in Limburg/Lahn, Germany; the strain wave gearing theory utilizes the flexibility of metal. The mechanism has three basic components: a wave generator, a flex spline, a circular spline. More complex versions have a fourth component used to shorten the overall length or to increase the gear reduction within a smaller diameter, but still follow the same basic principles; the wave generator is made up of two separate parts: an elliptical disk called a wave generator plug and an outer ball bearing. The gear plug is inserted into the bearing; the flex spline is shaped like a shallow cup. The sides of the spline are thin, but the bottom is rigid; this results in significant flexibility of the walls at the open end due to the thin wall, in the closed side being quite rigid and able to be secured.
Teeth are positioned radially around the outside of the flex spline. The flex spline fits over the wave generator, so that when the wave generator plug is rotated, the flex spline deforms to the shape of a rotating ellipse and does not slip over the outer elliptical ring of the ball bearing; the ball bearing lets the flex spline rotate independently to the wave generator's shaft. The circular spline is a rigid circular ring with teeth on the inside; the flex spline and wave generator are placed inside the circular spline, meshing the teeth of the flex spline and the circular spline. Because the flex spline is deformed into an elliptical shape, its teeth only mesh with the teeth of the circular spline in two regions on opposite sides of the flex spline. Assume that the wave generator is the input rotation; as the wave generator plug rotates, the flex spline teeth which are meshed with those of the circular spline change position. The major axis of the flex spline's ellipse rotates with wave generator, so the points where the teeth mesh revolve around the center point at the same rate as the wave generator's shaft.
The key to the design of the strain wave gear is that there are fewer teeth on the flex spline than there are on the circular spline. This means that for every full rotation of the wave generator, the flex spline would be required to rotate a slight amount backward relative to the circular spline, thus the rotation action of the wave generator results in a much slower rotation of the flex spline in the opposite direction. For a strain wave gearing mechanism, the gearing reduction ratio can be calculated from the number of teeth on each gear: reduction ratio = flex spline teeth − circular spline teeth flex spline teeth For example, if there are 202 teeth on the circular spline and 200 on the flex spline, the reduction ratio is /200 = −0.01 Thus the flex spline spins at 1/100 the speed of the wave generator plug and in the opposite direction. Different reduction ratios are set by changing the number of teeth; this can either be achieved by changing the mechanism's diameter or by changing the size of the individual teeth and thereby preserving its size and weight.
The range of possible gear ratios is limited by tooth size limits for a given configuration. The advantages include: no backlash, high compactness and light weight, high gear ratios, reconfigurable ratios within a standard housing, good resolution and excellent repeatability when repositioning inertial loads, high torque capability, coaxial input and output shafts. High gear reduction ratios are possible in a small volume. Cycloidal drive Peristaltic pump Harmonic drive function demonstration
A stair lift is a mechanical device for lifting people up and down stairs. For sufficiently wide stairs, a rail is mounted to the treads of the stairs. A chair or lifting platform is attached to the rail. A person gets onto the chair or platform and is lifted up or down the stairs by the chair which moves along the rail. Stair lifts are known variously as stair lifts, stair-lifts, chair lifts, stair gliders and by other names; this type of chair lift should not be confused with the chairlift used by skiers. The term stair climber can refer either to stair lifts, or more to the exercise equipment by the same name; some of the first stair lifts to be produced commercially were advertised and sold in the U. S. in the 1930s by the Inclinator Company of America. Many users at the time were victims of polio. Now they are seen for use in elderly, fall-prone individuals, the disabled who are unable to navigate stairs safely. In the 1920s, C. C. Crispen, a Pennsylvania entrepreneur, created a way to enable his ailing friend to travel from floor to floor.
Crispen's idea was to design a seat. A self-taught engineer, he built the first prototype of the inclining chair, he called it the Inclin-ator. Prior to this Frederick Muffett of Royal Tunbridge Wells and patented the "An Invalid Chair with Tramway for use on Staircases". However, TV historian Doctor David Starkey has in 2009, found evidence in a list of the possessions of King Henry VIII that attributes the first stairlift invented to the monarch; the 30 stone king, injured through jousting, used a chair, hauled up and down stairs on a block and tackle system by servants at the ancient Whitehall Palace in London. Modern stair lifts can be found with a wide variety of features such as adjustable seat height, battery isolation switches, call stations,'flip-up' rail, key switch, folding step, speed governor, seat belt, soft start and soft stop. Straight rails for use on domestic staircases are made from extruded aluminum or steel and come in various cross-sectional shapes; these rails may weigh over 30 kg, depending on the length.
In most applications they are attached to the steps with metal brackets. If a rail crosses a doorway at the bottom of the stairs or causes an obstruction a hinge can be fitted so the end of the rail can be folded back out of the way when not in use. Curved rails are made from materials such as steel or aluminum and come in various cross-sectional shapes according to the designer. Individual designs vary a lot and the key criterion is to make the curves with the smallest radius possible so they will wrap around objects such as newel posts; the sections of curved rails packaged well to prevent damage in transit and are unwrapped and assembled on site. Rails for wheelchair platform stair lifts may be secured to walls in addition to the step fixings; the carriage is the component which moves along the rail and runs on small diameter rollers. In most designs the carriage is pulled by a cable or chain, or driven along the inclined rail by a rack and pinion system or other drive arrangement. Most domestic carriages have a seat with a footrest.
Some special models have a stand-on platform known as a "perch" seat. For users with shorter legs a short seat can be fitted. Seats can be tailored to suit individual needs; the conventional layout for a typical domestic stair lift is to have the seat at right angles to the rail so the user travels "sidesaddle". At the top of the staircase the seat can be swiveled through around 45 degrees or 90 degrees locked in place to allow the user to alight from it onto a landing. Stair lifts are available with either a manual swivel or a powered swivel, depending on the users ability. Most swivel seats have a safety switch so the stair lift won’t move unless the seat is locked into its travel position. Special models with seats facing the bottom of the staircase have been produced for users with spinal or other conditions which prevent use of the conventional seat layout. More room is need on the landing with these special seats; these are the most common type of stair lifts used in private dwellings with straight stairs and have a straight rail, attached to the steps of the staircase.
Straight-rail stair lifts can be installed within days of being ordered and, having a rail, cut to length from a stock part, they are the least expensive stair lifts. Curved stair lifts are made to follow the shape of an individual staircase. On staircases with intermediate flat landings they eliminate the need for multiple straight stair lifts by providing a continuous ride up the entire length of the staircase; because the rail is custom-made to follow the staircase, because the chair is more complex that on a straight-rail stair lift, curved-rail stair lifts are more costly than stair lifts for straight stairs. Specifying a curved-rail stair lifts involves careful measurement and manufacturing, the installation process takes longer than for a straight domestic stair lift. One manufacturer can provide a curved-rail stair lift made from modular parts; this has the advantage of quick delivery time next day. The installer brings many picks from them, they are similar in price to a custom-made curved-rail stair lift.
Vertical platform lifts come under the general definition of a stair lift and are of a much heavier construction than a domestic stair lift due to the fact they are going to transport a wheelchair or scooter and the person. Most platform stair lifts are used in public
Canals, or navigations, are human-made channels, or artificial waterways, for water conveyance, or to service water transport vehicles. In most cases, the engineered works will have a series of dams and locks that create reservoirs of low speed current flow; these reservoirs are referred to as slack water levels just called levels. A canal is known as a navigation when it parallels a river and shares part of its waters and drainage basin, leverages its resources by building dams and locks to increase and lengthen its stretches of slack water levels while staying in its valley. In contrast, a canal cuts across a drainage divide atop a ridge requiring an external water source above the highest elevation. Many canals have been built at elevations towering over valleys and other water ways crossing far below. Canals with sources of water at a higher level can deliver water to a destination such as a city where water is needed; the Roman Empire's aqueducts were such water supply canals. A navigation is a series of channels that run parallel to the valley and stream bed of an unimproved river.
A navigation always shares the drainage basin of the river. A vessel uses the calm parts of the river itself as well as improvements, traversing the same changes in height. A true canal is a channel that cuts across a drainage divide, making a navigable channel connecting two different drainage basins. Most commercially important canals of the first half of the 19th century were a little of each, using rivers in long stretches, divide crossing canals in others; this is true for many canals still in use. Both navigations and canals use engineered structures to improve navigation: weirs and dams to raise river water levels to usable depths. Since they cut across drainage divides, canals are more difficult to construct and need additional improvements, like viaducts and aqueducts to bridge waters over streams and roads, ways to keep water in the channel. There are two broad types of canal: Waterways: canals and navigations used for carrying vessels transporting goods and people; these can be subdivided into two kinds:Those connecting existing lakes, other canals or seas and oceans.
Those connected in a city network: such as the Canal Grande and others of Venice Italy. Aqueducts: water supply canals that are used for the conveyance and delivery of potable water for human consumption, municipal uses, hydro power canals and agriculture irrigation. Canals were of immense importance to commerce and the development and vitality of a civilization. In 1855 the Lehigh Canal carried over 1.2 million tons of anthracite coal. The few canals still in operation in our modern age are a fraction of the numbers that once fueled and enabled economic growth, indeed were a prerequisite to further urbanization and industrialization – for the movement of bulk raw materials such as coal and ores are difficult and marginally affordable without water transport; such raw materials fueled the industrial developments and new metallurgy resulting of the spiral of increasing mechanization during 17th–20th century, leading to new research disciplines, new industries and economies of scale, raising the standard of living for any industrialized society.
The surviving canals, including most ship canals, today service bulk cargo and large ship transportation industries, whereas the once critical smaller inland waterways conceived and engineered as boat and barge canals have been supplanted and filled in, abandoned and left to deteriorate, or kept in service and staffed by state employees, where dams and locks are maintained for flood control or pleasure boating. Their replacement was gradual, beginning first in the United States in the mid-1850s where canal shipping was first augmented by began being replaced by using much faster, less geographically constrained & limited, cheaper to maintain railways. By the early 1880s, canals which had little ability to economically compete with rail transport, were off the map. In the next couple of decades, coal was diminished as the heating fuel of choice by oil, growth of coal shipments leveled off. After World War I when motor-trucks came into their own, the last small U. S. barge canals saw a steady decline in cargo ton-miles alongside many railways, the flexibility and steep slope climbing capability of lorries taking over cargo hauling as road networks were improved, which had the freedom to make deliveries well away from rail lined road beds or ditches in the dirt which couldn't operate in the winter.
Canals are built in one of three ways, or a combination of the three, depending on available water and available path: Human made streamsA canal can be created where no stream presently exists. Either the body of the canal is dug or the sides of the canal are created by making dykes or levees by piling dirt, concrete or other building materials; the finished shape of the canal as seen in cross section is known as the canal prism. The water for the canal must be provided like streams or reservoirs. Where the new waterway must change elevation engineering works like locks, lifts or elevators are constructed to raise and lower vessels. Examples include canals that connect valleys over a higher body of land, like Canal du Midi, Canal de Briare and the Panama Canal. A canal can be constructed by dredging a channel in the bottom of an existing lake; when the channel is complete, the lake is drained and the channel becom
An epicyclic gear train consists of two gears mounted so that the centre of one gear revolves around the centre of the other. A carrier connects the centres of the two gears and rotates to carry one gear, called the planet gear, around the other, called the sun gear; the planet and sun gears mesh. A point on the pitch circle of the planet gear traces an epicycloid curve. In this simplified case, the sun gear is the planetary gear roll around the sun gear. An epicyclic gear train can be assembled so the planet gear rolls on the inside of the pitch circle of a fixed, outer gear ring, or ring gear, sometimes called an annular gear. In this case, the curve traced by a point on the pitch circle of the planet is a hypocycloid; the combination of epicycle gear trains with a planet engaging both a sun gear and a ring gear is called a planetary gear train. In this case, the ring gear is fixed and the sun gear is driven. Epicyclic gears get their name from their earliest application, the modelling of the movements of the planets in the heavens.
Believing the planets, as everything in the heavens, to be perfect, they could only travel in perfect circles, but their motions as viewed from Earth could not be reconciled with circular motion. At around 500 BC, the Greeks invented the idea of epicycles, of circles travelling on the circular orbits. With this theory Claudius Ptolemy in the Almagest in 148 AD was able to predict planetary orbital paths; the Antikythera Mechanism, circa 80 BC, had gearing, able to approximate the moon's elliptical path through the heavens, to correct for the nine-year precession of that path. Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear; the planet gears are mounted on a movable arm or carrier, which itself may rotate relative to the sun gear. Epicyclic gearing systems incorporate the use of an outer ring gear or annulus, which meshes with the planet gears. Planetary gears are classified as simple or compound planetary gears.
Simple planetary gears have one sun, one ring, one carrier, one planet set. Compound planetary gears involve one or more of the following three types of structures: meshed-planet, stepped-planet, multi-stage structures. Compared to simple planetary gears, compound planetary gears have the advantages of larger reduction ratio, higher torque-to-weight ratio, more flexible configurations; the axes of all gears are parallel, but for special cases like pencil sharpeners and differentials, they can be placed at an angle, introducing elements of bevel gear. Further, the sun, planet carrier and ring axes are coaxial. Epicyclic gearing is available which consists of a sun, a carrier, two planets which mesh with each other. One planet meshes with the sun gear. For this case, when the carrier is fixed, the ring gear rotates in the same direction as the sun gear, thus providing a reversal in direction compared to standard epicyclic gearing. In the 2nd-century AD treatise Almagest, Ptolemy used rotating deferent and epicycles that form epicyclic gear trains to predict the motions of the planets.
Accurate predictions of the movement of the Sun and the five planets, Venus, Mars and Saturn, across the sky assumed that each followed a trajectory traced by a point on the planet gear of an epicyclic gear train. This curve is called an epitrochoid. Epicyclic gearing was used in the Antikythera Mechanism, circa 80 BCE, to adjust the displayed position of the moon for the ellipticity of its orbit, for the apsidal precession of its orbit. Two facing gears were rotated around different centers, one drove the other not with meshed teeth but with a pin inserted into a slot on the second; as the slot drove the second gear, the radius of driving would change, thus invoking a speeding up and slowing down of the driven gear in each revolution. Richard of Wallingford, an English abbot of St Albans monastery is credited for reinventing epicyclic gearing for an astronomical clock in the 14th century. In 1588, Italian military engineer Agostino Ramelli invented the bookwheel, a vertically-revolving bookstand containing epicyclic gearing with two levels of planetary gears to maintain proper orientation of the books.
The gear ratio of an epicyclic gearing system is somewhat non-intuitive because there are several ways in which an input rotation can be converted into an output rotation. The three basic components of the epicyclic gear are: Sun: The central gear Carrier: Holds one or more peripheral Planet gears, all of the same size, meshed with the sun gear Ring or Annulus: An outer ring with inward-facing teeth that mesh with the planet gear or gearsThe overall gear ratio of a simple planetary gearset can be calculated using the following two equations, representing the sun-planet and planet-ring interactions respectively: N s ω s + N p ω p − ω c = 0
The grade of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope. A larger number indicates higher or steeper degree of "tilt". Slope is calculated as a ratio of "rise" to "run", or as a fraction in which run is the horizontal distance and rise is the vertical distance; the grades or slopes of existing physical features such as canyons and hillsides and river banks and beds are described. Grades are specified for new linear constructions; the grade may refer to the perpendicular cross slope. There are several ways to express slope: as an angle of inclination to the horizontal; as a percentage, the formula for, 100 rise run which could be expressed as the tangent of the angle of inclination times 100. In the U. S. this percentage "grade" is the most used unit for communicating slopes in transportation, surveying and civil engineering. As a per mille figure, the formula for, 1000 rise run which could be expressed as the tangent of the angle of inclination times 1000.
This is used in Europe to denote the incline of a railway. As a ratio of one part rise to so many parts run. For example, a slope that has a rise of 5 feet for every 100 feet of run would have a slope ratio of 1 in 20.. This is the method used to describe railway grades in Australia and the UK, it is used for roads in Hong Kong, was used for roads in the UK until the 1970s. As a ratio of many parts run to one part rise, the inverse of the previous expression. For example, "slopes are expressed as ratios such as 4:1; this means that for every 4 units of horizontal distance there is a 1-unit vertical change either up or down."Any of these may be used. Grade is expressed as a percentage, but this is converted to the angle α from horizontal or the other expressions. Slope may still be expressed when the horizontal run is not known: the rise can be divided by the hypotenuse; this is not the usual way to specify slope. But in practice the usual way to calculate slope is to measure the distance along the slope and the vertical rise, calculate the horizontal run from that.
When the angle of inclination is small, using the slope length rather than the horizontal displacement makes only an insignificant difference. Railway gradients are expressed in terms of the rise in relation to the distance along the track as a practical measure. In cases where the difference between sin and tan is significant, the tangent is used. In any case, the following identity holds for all inclinations up to 90 degrees: tan α = sin α 1 − sin 2 α. In Europe, road gradients are signed as a percentage. Grades are related using the following equations with symbols from the figure at top. Tan α = Δ h d This ratio can be expressed as a percentage by multiplying by 100. Α = arctan Δ h d If the tangent is expressed as a percentage, the angle can be determined as: α = arctan % slope 100 If the angle is expressed as a ratio then: α = arctan 1 n In vehicular engineering, various land-based designs are rated for their ability to ascend terrain. Trains rate much lower than automobiles.
The highest grade a vehicle can ascend while maintaining a particular speed is sometimes termed that vehicle's "gradeability". The lateral slopes of a highway geometry are sometimes called fills or cuts where these techniques have been used to create them. In the United States, maximum grade for Federally funded highways is specified in a design table based on terrain and design speeds, with up to 6% allowed in mountainous areas and hilly urban areas with exceptions for up to 7% grades on mountainous roads with speed limits below 60 mph; the steepest roads in the world are Baldwin Street in Dunedin, New Zealand, Ffordd Pen Llech in Harlech and Canton Avenue in Pittsburgh, Pennsylvania. The Guinness World R