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64-411: The original Hondamatic, like all following Honda automatics, featured gears on parallel axes rather than planetary gears like most other automatic transmissions. The two gears for each ratio - one driving and the other driven - are in constant mesh and each ratio is engaged by a dedicated clutch connected to one of the ratio's two gears. The clutches are hydraulically controlled, applying oil pressure to

128-430: A combined point-shaping cone that is aligned to the cylindrical pencil alignment guide hole, into which the pencil is inserted. A sharp blade is mounted so that its sharp edge just enters the shaping cone tangentially . The pencil is inserted into the sharpener and rotated while the sharpener is held motionless. The body of the sharpener is often contoured, ridged or grooved to make the small block easier to firmly grip, and

192-509: A desk or wall and powered by a hand crank . Typically, the pencil is inserted into the sharpener with one hand, and the crank is turned with the other. This rotates a set of helical cylindrical cutters in the mechanism, set at an acute angle to each other. The multiple cutting edges quickly sharpen the pencil, with a more precise finish than a single-blade device . Some cylindrical sharpeners have only one helical cutter cylinder , but most have two cylinders or more. Most planetary sharpeners have

256-469: A device to precisely sharpen the pencils. The device of Mr. Boucher was technically sensible and functional. His idea was also internationally known and recognized, as shown by corresponding reports in German literature at this time. But Mr. Boucher had not applied a patent for his pencil sharpener. Commercial use of his inventions is unlikely. French mathematician Bernard Lassimonne (Limoges) applied for

320-598: A few pencil sharpeners as a gift in the late 1980s and kept them organized into categories, including cats, Christmas, and Disneyland . So-called "prism" sharpeners, also called "manual" or "pocket" sharpeners in the United States, have no separate moving parts and are typically the smallest and cheapest commonly used pencil sharpener on the market. The simplest common variety is a small rectangular prism or block, only about 1 × 5/8 × 7/16 inch (2.5 × 1.7 × 1.1 cm) in size. The block-shaped sharpener consists of

384-479: A gear with "dogs" to change gear engagement, the same as on a non-Hondamatic motorcycle transmission. Applications: Honda also applies the Hondamatic name to a hydraulic piston-based continuously variable transmission used in motorscooters , all-terrain vehicles , and other types of power equipment . Applications Planetary gear An epicyclic gear train (also known as a planetary gearset )

448-402: A large opening, with a rotatable guide disk in front of it that has multiple holes of different sizes, to accommodate pencils of many different diameters. Advanced models have a spring-driven holder for the pencil, so that the pencil automatically is pushed into the mechanism while being sharpened. Some versions also offer a regulator of the desired sharpness, since it is not always desired to make

512-410: A planetary gear train begins by considering the speed ratio of the gear train when the carrier is held fixed. This is known as the fixed carrier train ratio. In the case of a simple planetary gear train formed by a carrier supporting a planet gear engaged with a sun and ring gear, the fixed carrier train ratio is computed as the speed ratio of the gear train formed by the sun, planet and ring gears on

576-492: A round pencil, abandoning some distinctive aspects of the carpenter's pencil. Alternatively, a special carpenter's pencil sharpener can be used, which has a sliding mechanism that leaves flat facets on the lead, in a manner similar to hand sharpening with a sharp knife. Mechanical pencils with thin diameter leads dispense the graphite lead progressively during use and thus do not require sharpening; such pencils are sometimes called "self-sharpening". A type of mechanical pencil has

640-514: A shaft connection between two planets in each planet train), and multi-stage structures (the system contains two or more planet sets). Compared to simple planetary gears, compound planetary gears have the advantages of larger reduction ratio, higher torque-to-weight ratio, and more flexible configurations. The axes of all gears are usually parallel, but for special cases like pencil sharpeners and differentials , they can be placed at an angle, introducing elements of bevel gear (see below). Further,

704-429: A single blade for use on wax crayons are available, and sometimes included in boxes of crayons. These often have plastic blades, which are adequate for the soft wax. An artist's or draftsman's pencil sharpener leaves the graphite untouched and sharpens only the wood (some models can switch from standard to wood-only by an adjustment). The graphite lead is then honed to a sharp point with a lead pointer, which sharpens only

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768-526: A three-speed. The true three-speed H3 was launched in 1979. In 1982 Honda introduced a four-speed fully-automatic (called Hondamatic Full-Auto ), followed by a fully-automatic three-speed in 1983. The semi-automatic version continued to be available in Honda's smaller cars, where it was gradually replaced by conventional automatics. With the 1988 remake of the Honda Acty/Street , the last Hondamatic

832-399: Is a gear reduction assembly consisting of two gears mounted so that the center of one gear (the "planet") revolves around the center of the other (the "sun"). A carrier connects the centers of the two gears and rotates, to carry the planet gear(s) around the sun gear. The planet and sun gears mesh so that their pitch circles roll without slip. If the sun gear is held fixed, then a point on

896-401: Is a larger clearance hole at the end of the cone allowing sections of the pencil lead which break away to be removed with only minor inconvenience. Prism sharpeners can be bare or enclosed in a container to collect the shavings, while some enclosed sharpeners may be harder to clear in the event of a blockage. A few prism sharpeners are hand-cranked, rotating the cutting blade instead of rotating

960-468: Is a whole number If one is to create an asymmetric carrier frame with non-equiangular planet gears, say to create some kind of mechanical vibration in the system, one must make the teething such that the above equation complies with the "imaginary gears". For example, in the case where a carrier frame is intended to contain planet gears spaced 0°, 50°, 120°, and 230°, one is to calculate as if there are actually 36 planetary gears (10° equiangular), rather than

1024-422: Is constructed from two identical coaxial epicyclic gear trains assembled with a single carrier such that their planet gears are engaged. This forms a planetary gear train with a fixed carrier train ratio R  = −1. In this case, the fundamental formula for the planetary gear train yields, or Thus, the angular velocity of the carrier of a spur gear differential is the average of the angular velocities of

1088-405: Is stationary); one of the two remaining components is an input , providing power to the system, while the last component is an output , receiving power from the system. The ratio of input rotation to output rotation is dependent upon the number of teeth in each of the gears, and upon which component is held stationary. Alternatively, in the special case where the number of teeth on each gear meets

1152-504: Is the Boston Polar Club pencil sharpener, introduced around 1936. Electric pencil sharpeners work on the same principle as manual ones, but one or more flat-bladed or cylindrical cutters are rotated by an electric motor . Some electric pencil sharpeners are powered by batteries rather than being plugged into a building's electrical system, making them more portable. Auto-stop electric pencil sharpeners are able to sense when

1216-610: Is the lowest gear ratio attainable with an epicyclic gear train. This type of gearing is sometimes used in tractors and construction equipment to provide high torque to the drive wheels. In bicycle hub gears , the sun is usually stationary, being keyed to the axle or even machined directly onto it. The planetary gear carrier is used as input. In this case the gear ratio is simply given by N s + N r N r   . {\displaystyle {\tfrac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{r}}}}~.} The number of teeth in

1280-583: Is too large, the tip of the pencil will repeatedly break off. Prism sharpeners may be right- or left-handed, requiring clockwise or counter-clockwise rotation of the pencil being sharpened. Unlike prism sharpeners, linear blade sharpeners do not rotate relative to the pencil being sharpened, and may be viewed as just a special form of knife, with a mechanical guide for increased safety and convenience. Some models use replaceable shaving razor blades , while others have permanently-fitted blades. Linear blade sharpeners may require more skill, but they allow one to sharpen

1344-441: Is typically made of aluminum alloy , magnesium alloy or hard plastic . The blade inside the sharpener shaves the wood and graphite tip of the pencil, while the shavings emerge through a slot along the blade edge. It is important that the cylindrical alignment hole closely fits the diameter of the pencil, to keep the pencil from wobbling, which would cause stepped or lurching cut-depths and point breakage. Another important feature

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1408-488: The bookwheel , a vertically revolving bookstand containing epicyclic gearing with two levels of planetary gears to maintain proper orientation of the books. French mathematician and engineer Desargues designed and constructed the first mill with epicycloidal teeth c.  1650 . In order that the planet gear teeth mesh properly with both the sun and ring gears, assuming n p {\displaystyle n_{\text{p}}} equally spaced planet gears,

1472-505: The 1830s and 1840s, some French people, all based in Paris, were engaged in construction of simple pencil sharpening tools, like François Joseph Lahausse. These devices were partially sold, but without supra-regional significance. In 1847, the French nobleman Thierry des Estivaux invented a simple hand-held pencil sharpener in its recognizable modern form. The first American pencil sharpener

1536-470: The 500cc Honda S500 and one that was able to be reliable at a maximum engine speed of 8000rpm. This led Honda to design its own transmission. They purchased a transmission from Borg-Warner for the purpose of developing an original transmission design. They tested their newly developed automatic transmission on the L700. When testing and refinements had been made, Honda sold their first automatic transmission in

1600-614: The Greeks invented the idea of epicycles, of circles travelling on the circular orbits. With this theory Claudius Ptolemy in the Almagest in 148 CE was able to approximate planetary paths observed crossing the sky. The Antikythera Mechanism , circa 80 BCE, had gearing which was able to closely match the Moon's elliptical path through the heavens, and even to correct for the nine-year precession of that path. (The Greeks interpreted

1664-557: The N360. The Hondamatic was later used in Honda's 400, 450 and 750 cc motorcycles . In this application, it was not a true automatic transmission, as the driver had to manually select one of the two gears. The transmission of the 750 Hondamatics incorporated two hydraulically-controlled clutches (one for each gear), with the foot-operated gear selector operating the hydraulic valve. The 400/450 Hondamatics, however, have no clutches at all. The foot-operated gear selector physically moves

1728-703: The US Automatic Pencil Sharpener after 1907, which dominated in those years. They later sold machines with milling mechanisms, such as the Climax, Dexter, Wizard, and Junior models. In the next few decades, APSCO became the largest pencil sharpening machine producer in the world and together with a few other US companies, it dominated the market. Electric pencil sharpeners for offices have been made since at least 1917. A school teacher, Neil Carruthers, brought electric sharpeners from his visit to USA back to his town of Whitehaven for use in schools at

1792-400: The desired "gear". Shifting between forward gears was done by simply sliding the gear selector (actually a hydraulic valve) from 1 to 2. It did not automatically shift, but because of the torque converter, could be driven entirely in second gear. The Honda automobile torque converter had a lockup , leading the company to sell the original Hondamatic (which had just two forward gear ratios) as

1856-620: The end of the Victorian Era. In May 2011, tourism officials in Logan, Ohio put on display, in its regional welcome center, hundreds of pencil sharpeners which had been collected by Rev. Paul Johnson, an Ohio minister who died in 2010. Johnson, a World War II veteran, had kept his collection of more than 3,400 sharpeners in a small shed, outside his home in Carbon Hill in southeast Ohio. He had started collecting after his wife gave him

1920-406: The fixed carrier. This is given by In this calculation the planet gear is an idler gear. The fundamental formula of the planetary gear train with a rotating carrier is obtained by recognizing that this formula remains true if the angular velocities of the sun, planet and ring gears are computed relative to the carrier angular velocity. This becomes, This formula provides a simple way to determine

1984-401: The flattened shape of which stops them from rolling away, while still providing a constant line width. These pencils were traditionally sharpened with tools conveniently to hand, such as a plane or sandpaper. Rotating pencil sharpeners are now available for these pencils, in which a rotating plastic collar holds the pencil in position, although they then sharpen to the usual conical point as for

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2048-399: The following equation must be satisfied: where N s , N r {\displaystyle N_{\text{s}},N_{\text{r}}} are the number of teeth of the sun gear and the ring gear , respectively and n p {\displaystyle n_{\text{p}}} is the number of planet gears in the assembly and A {\displaystyle A}

2112-414: The following: and only if ω r ≠ ω c   . {\displaystyle \omega _{\text{r}}\neq \omega _{\text{c}}~.} In many epicyclic gearing systems, one of these three basic components is held stationary (hence set ω ... = 0 {\displaystyle \omega _{\text{...}}=0} for whichever gear

2176-477: The four real ones. The gear ratio of an epicyclic gearing system is somewhat non-intuitive, particularly because there are several ways in which an input rotation can be converted into an output rotation. The four basic components of the epicyclic gear are: The 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: where from which we can derive

2240-432: The graphite core needle-sharp. Some older models like the 1897 German Jupiter 1 used reversible rotary cutter-disks with cutting edges radiating from the center on each side. These were high-end models, quite large and expensive. Others simply used abrasives like sandpaper . In some cases an abrasive was used to shape the graphite core, while the wood was cut some other way. The oldest surviving electric pencil sharpener

2304-401: The internal gear mate that is typical of a ring gear. Some epicyclic gear trains employ two planetary gears which mesh with each other. One of these planets meshes with the sun gear, the other planet meshes with the ring gear. This results in different ratios being generated by the planetary and also causes the sun gear to rotate in the same direction as the ring gear when the planet carrier is

2368-438: The lead without wood. Lead pointers are also used with mechanical leadholders , with thicker diameter leads like 2 mm which have removable/refillable leads. Some sharpeners which function as a long point sharpener, have a second hole in which the blade sharpens the untouched graphite to a long, more precise point than would be otherwise possible using a single hole long point sharpener. Carpenters may use carpenter pencils ,

2432-749: The market. These devices were often heavy and intended for use in offices. Examples are the Perfect Pencil Pointer (Goodell. Co.), the GEM Pencil Sharpener (by Gould & Cook Co.), the Planetary Pencil Sharpener (A. B. Dick Co.), all from the US or the Jupiter (Guhl & Harbeck Co.) from Germany. At the beginning of the 20th century the company Automatic Pencil Sharpener Co. (APSCO) was founded and brought out

2496-468: The motion they saw, not as elliptical, but rather as epicyclic motion.) In the 2nd century AD treatise The Mathematical Syntaxis (a.k.a. Almagest ), Claudius 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, Moon, and the five planets, Mercury, Venus, Mars, Jupiter, and Saturn, across

2560-466: 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, later described epicyclic gearing for an astronomical clock in the 14th century. In 1588, Italian military engineer Agostino Ramelli invented

2624-453: The pencil shavings debris into a bin. Before the development of dedicated pencil sharpeners, a pencil was sharpened by whittling with a knife . The development of pencil sharpeners began in France when a French book from 1822 reported in detail about an invention of Mr. C. A. Boucher (Paris) for the construction of a pencil sharpener. He was working with pantographs and apparently needed

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2688-404: The pencil. Moderate care is needed to not break the tip of the pencil being sharpened, requiring the pencil to be sharpened again. However, because pencils may have different standard diameters in different nations, imported sharpeners may have non-standard-sized alignment guide-holes, making sharpening attempts difficult. If the alignment hole is too small, the pencil cannot be inserted, while if it

2752-416: The pitch circle of the planet gear traces an epicycloid curve. An epicyclic gear train can be assembled so the planet gear rolls on the inside of the pitch circle of an outer gear ring, or ring gear, sometimes called an annulus gear . Such an assembly of a planet engaging both a sun gear and a ring gear is called a planetary gear train . By choosing to hold one component or another—the planetary carrier,

2816-705: The planet gear is irrelevant. From the above formulae, we can also derive the accelerations of the sun, ring and carrier, which are: In epicyclic gears, two speeds must be known in order to determine the third speed. However, in a steady state condition, only one torque must be known in order to determine the other two torques. The equations which determine torque are: where: τ r {\displaystyle \tau _{r}} — Torque of ring (annulus), τ s {\displaystyle \tau _{s}} — Torque of sun, τ c {\displaystyle \tau _{c}} — Torque of carrier. For all three, these are

2880-472: The planet gear(s) about its axis. Rotation of the planet gears can in turn drive the ring gear (not depicted in diagram), at a speed corresponding to the gear ratios: If the ring gear has N r {\displaystyle \,N_{\text{r}}\,} teeth, then the ring will rotate by N p N r {\displaystyle \,{\tfrac {\,N_{\text{p}}\,}{N_{\text{r}}}}\,} turns for each turn of

2944-533: The planetary gears. For instance, if the ring gear has 64 teeth, and the planets 16 teeth, one clockwise turn of a planet gear results in ⁠ 16 / 64  ⁠ , or ⁠ 1 / 4  ⁠ clockwise turns of the ring gear. Extending this case from the one above: So, with the planetary carrier locked, one turn of the sun gear results in − N s N r {\displaystyle \;-{\tfrac {\,N_{\text{s}}\,}{N_{\text{r}}}}\;} turns of

3008-461: The ratio is equal to − N s N p . {\displaystyle -{\tfrac {\,N_{\text{s}}\,}{N_{\text{p}}}}\;.} For instance, if the sun gear has 24 teeth, and each planet has 16 teeth, then the ratio is ⁠− + 24 / 16  ⁠ , or ⁠− + 3 / 2  ⁠ ; this means that one clockwise turn of the sun gear produces 1.5  counterclockwise turns of each of

3072-415: The relationship N r = N s + 2 N p , {\displaystyle \,N_{\text{r}}=N_{\text{s}}+2\,N_{\text{p}}\;,} the equation can be re-written as the following: where These relationships can be used to analyze any epicyclic system, including those, such as hybrid vehicle transmissions, where two of the components are used as inputs with

3136-692: The ring gear is held stationary and the sun gear is used as the input, the planet carrier will be the output. The gear ratio in this case will be 1 / ( 1 + N r N s ) = N s N s + N r , {\displaystyle \,1/\left(1+{\tfrac {\,N_{\text{r}}\,}{N_{\text{s}}}}\right)={\tfrac {N_{\text{s}}}{\,N_{\text{s}}+N_{\text{r}}\,}}\;,} which may also be written as N s : N s + N r   . {\displaystyle \;N_{\text{s}}:N_{\text{s}}+N_{\text{r}}~.} This

3200-439: The ring gear, or the sun gear—stationary, three different gear ratios can be realized. Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer, or planet , gears or pinions , revolving about a central sun gear or sun wheel . Typically, the planet gears are mounted on a movable arm or carrier , which itself may rotate relative to the sun gear. Epicyclic gearing systems also incorporate

3264-539: The ring gear. The ring gear may also be held fixed, with input provided to the planetary gear carrier; output rotation is then produced from the sun gear. This configuration will produce an increase in gear ratio, equal to 1 + N r N s = N s + N r N s   . {\displaystyle \;1+{\tfrac {\,N_{\text{r}}\,}{N_{\text{s}}}}={\tfrac {\,N_{\text{s}}+N_{\text{r}}\,}{N_{\text{s}}}}~.} If

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3328-507: 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 , and even for its orbital apsidal precession . Two facing gears were rotated around slightly different centers; one drove

3392-476: The speed ratios for the simple planetary gear train under different conditions: 1. The carrier is held fixed, ω c =0, 2. The ring gear is held fixed, ω r =0, 3. The sun gear is held fixed, ω s =0, Each of the speed ratios available to a simple planetary gear train can be obtained by using band brakes to hold and release the carrier, sun or ring gears as needed. This provides the basic structure for an automatic transmission . A spur gear differential

3456-471: The stationary. The fundamental equation becomes: Pencil sharpeners A pencil sharpener (or pencil pointer , or in Ireland a parer or topper ) is a tool for sharpening a pencil 's writing point by shaving away its worn surface. Pencil sharpeners may be operated manually or by an electric motor . It is common for many sharpeners to have a casing around them, which can be removed for emptying

3520-410: The sun and ring gears. In discussing the spur gear differential, the use of the term ring gear is a convenient way to distinguish the sun gears of the two epicyclic gear trains. Ring gears are normally fixed in most applications as this arrangement will have a good reduction capacity. The second sun gear serves the same purpose as the ring gear of a simple planetary gear train but clearly does not have

3584-471: The sun, planet carrier and ring axes are usually coaxial . Epicyclic gearing is also available which consists of a sun, a carrier, and two planets which mesh with each other. One planet meshes with the sun gear, while the second planet meshes with the ring 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. Around 500 BCE,

3648-554: The third providing output relative to the two inputs. In one arrangement, the planetary carrier (green in the diagram above) is held stationary, and the sun gear (yellow) is used as input. In that case, the planetary gears simply rotate about their own axes (i.e., spin) at a rate determined by the number of teeth in each gear. If the sun gear has N s {\displaystyle \,N_{\text{s}}\,} teeth, and each planet gear has N p {\displaystyle \,N_{\text{p}}\,} teeth, then

3712-503: The tip of the pencil into any desired shape and angle of taper, whereas prism sharpeners have a fixed sharpening angle and produce circular symmetry. While most linear blade sharpeners are simple and directly hand-operated, some devices in the past were crank-operated, using mechanisms to convert crank rotation into linear motion. These mechanisms are also called planetary sharpeners , in reference to their use of planetary gears . A larger, stationary planetary sharpener can be mounted on

3776-466: The tip of the pencil is long enough, so they stop automatically. In basic automatic pencil sharpeners, the lead may become too long and break, and so users must be careful to supervise the operation. Specialized sharpeners are available that operate on non-standard sizes of pencil-shaped markers, such as wax crayons used in primary schools. Sharpeners that have two openings, one for normal pencils and one for larger crayons, are fairly common. Sharpeners with

3840-425: The torques applied to the mechanism (input torques). Output torques have the reverse sign of input torques. These torque ratios can be derived using the law of conservation of energy. Applied to a single stage this equation is expressed as: In the cases where gears are accelerating, or to account for friction, these equations must be modified. A convenient approach to determine the various speed ratios available in

3904-478: The use of an outer ring gear or annulus , which meshes with the planet gears. Planetary gears (or epicyclic gears) are typically classified as simple or compound planetary gears. Simple planetary gears have one sun, one ring, one carrier, and one planet set. Compound planetary gears involve one or more of the following three types of structures: meshed-planet (there are at least two more planets in mesh with each other in each planet train), stepped-planet (there exists

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3968-515: The world's first patent (French patent #2444) on a pencil sharpener in 1828. Pencil sharpener devices using his patent were actually produced and sold by Binant, a shop for painting accessories in Paris. In 1833 in England, Cooper & Eckstein patented the so-called Styloxynon, a simple device consisting of two sharp files set together at right angle in a small block of rosewood. This is the oldest pencil sharpener that has surviving examples. In

4032-403: Was discontinued. Applications: Honda could not make a conventional planetary gearset automatic transmission without infringing on any patents. Honda eventually asked Borg-Warner to design a prototype transmission for their upcoming vehicles. However, Borg-Warner declined. This was due to Borg-Warner not having transmission specifications that were efficient enough for such a small engine like

4096-501: Was patented by Walter Kittredge Foster of Bangor, Maine in 1855. He founded a company – the first pencil sharpener company in the world – and produced such small hand-held pencil sharpeners in a large amount. Only a few years later the sharpeners were sold also in Europe as "American pencil sharpeners". At the end of the 19th century, especially in the United States, pencil sharpeners with various mechanisms had been developed and put on

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