Toyota Variable Induction System , or T-VIS , is a variable intake system designed by Toyota to improve the low-end performance of multi-valve engines.
82-402: T-VIS is intended to improve the low-end torque of high-performance, four-stroke internal combustion engines - by changing the geometry of the intake manifold according to the engine rotation speed. The system uses two separate intake runners per cylinder , one being equipped with a butterfly valve that can either open or close the runner. All valves are attached to a common shaft which
164-534: A force is allowed to act through a distance, it is doing mechanical work . Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass , the work W can be expressed as W = ∫ θ 1 θ 2 τ d θ , {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \ \mathrm {d} \theta ,} where τ
246-570: A professional engineer or a chartered engineer . "Only a licensed engineer, for instance, may prepare, sign, seal and submit engineering plans and drawings to a public authority for approval, or to seal engineering work for public and private clients." This requirement can be written into state and provincial legislation, such as in the Canadian provinces, for example the Ontario or Quebec's Engineer Act. In other countries, such as Australia, and
328-718: A certain leverage. Today, torque is referred to using different vocabulary depending on geographical location and field of study. This article follows the definition used in US physics in its usage of the word torque . In the UK and in US mechanical engineering , torque is referred to as moment of force , usually shortened to moment . This terminology can be traced back to at least 1811 in Siméon Denis Poisson 's Traité de mécanique . An English translation of Poisson's work appears in 1842. A force applied perpendicularly to
410-675: A course in an engineering trade like fitter from the Industrial Training Institute (ITIs) to receive a "ITI Trade Certificate" and also pass the All India Trade Test (AITT) with an engineering trade conducted by the National Council of Vocational Training (NCVT) by which one is awarded a "National Trade Certificate". A similar system is used in Nepal. Some mechanical engineers go on to pursue
492-452: A drafter or draftsman. Drafting has historically been a two-dimensional process, but computer-aided design (CAD) programs now allow the designer to create in three dimensions. Instructions for manufacturing a part must be fed to the necessary machinery, either manually, through programmed instructions, or through the use of a computer-aided manufacturing (CAM) or combined CAD/CAM program. Optionally, an engineer may also manually manufacture
574-517: A failure has occurred, or when designing to prevent failure. Engineers often use online documents and books such as those published by ASM to aid them in determining the type of failure and possible causes. Once theory is applied to a mechanical design, physical testing is often performed to verify calculated results. Structural analysis may be used in an office when designing parts, in the field to analyze failed parts, or in laboratories where parts might undergo controlled failure tests. Thermodynamics
656-893: A field during the Industrial Revolution in Europe in the 18th century; however, its development can be traced back several thousand years around the world. In the 19th century, developments in physics led to the development of mechanical engineering science. The field has continually evolved to incorporate advancements; today mechanical engineers are pursuing developments in such areas as composites , mechatronics , and nanotechnology . It also overlaps with aerospace engineering , metallurgical engineering , civil engineering , structural engineering , electrical engineering , manufacturing engineering , chemical engineering , industrial engineering , and other engineering disciplines to varying amounts. Mechanical engineers may also work in
738-411: A force applied) the object being analyzed either breaks or is deformed plastically , depending on the criterion for failure. Fatigue failure occurs when an object fails after a number of repeated loading and unloading cycles. Fatigue failure occurs because of imperfections in the object: a microscopic crack on the surface of the object, for instance, will grow slightly with each cycle (propagation) until
820-408: A lever multiplied by its distance from the lever's fulcrum (the length of the lever arm ) is its torque. Therefore, torque is defined as the product of the magnitude of the perpendicular component of the force and the distance of the line of action of a force from the point around which it is being determined. In three dimensions, the torque is a pseudovector ; for point particles , it is given by
902-418: A line), so torque may be defined as that which produces or tends to produce torsion (around an axis). It is better to use a term which treats this action as a single definite entity than to use terms like " couple " and " moment ", which suggest more complex ideas. The single notion of a twist applied to turn a shaft is better than the more complex notion of applying a linear force (or a pair of forces) with
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#1732780235581984-492: A machine is likely to work. Engineers may seek license by a state, provincial, or national government. The purpose of this process is to ensure that engineers possess the necessary technical knowledge, real-world experience, and knowledge of the local legal system to practice engineering at a professional level. Once certified, the engineer is given the title of Professional Engineer (United States, Canada, Japan, South Korea, Bangladesh and South Africa), Chartered Engineer (in
1066-593: A minimum of 4 years post graduate on the job competency development and a peer-reviewed project report to become a Chartered Mechanical Engineer (CEng, MIMechE) through the Institution of Mechanical Engineers . CEng MIMechE can also be obtained via an examination route administered by the City and Guilds of London Institute . In most developed countries, certain engineering tasks, such as the design of bridges, electric power plants, and chemical plants, must be approved by
1148-1011: A part using the technical drawings. However, with the advent of computer numerically controlled (CNC) manufacturing, parts can now be fabricated without the need for constant technician input. Manually manufactured parts generally consist of spray coatings , surface finishes, and other processes that cannot economically or practically be done by a machine. Drafting is used in nearly every subdiscipline of mechanical engineering, and by many other branches of engineering and architecture. Three-dimensional models created using CAD software are also commonly used in finite element analysis (FEA) and computational fluid dynamics (CFD). Many mechanical engineering companies, especially those in industrialized nations, have incorporated computer-aided engineering (CAE) programs into their existing design and analysis processes, including 2D and 3D solid modeling computer-aided design (CAD). This method has many benefits, including easier and more exhaustive visualization of products,
1230-406: A postgraduate degree such as a Master of Engineering , Master of Technology , Master of Science , Master of Engineering Management (M.Eng.Mgt. or M.E.M.), a Doctor of Philosophy in engineering (Eng.D. or Ph.D.) or an engineer's degree . The master's and engineer's degrees may or may not include research . The Doctor of Philosophy includes a significant research component and is often viewed as
1312-478: A separate field within engineering. They brought with them manufacturing machines and the engines to power them. The first British professional society of mechanical engineers was formed in 1847 Institution of Mechanical Engineers , thirty years after the civil engineers formed the first such professional society Institution of Civil Engineers . On the European continent , Johann von Zimmermann (1820–1901) founded
1394-762: A single point particle is: L = r × p {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} } where p is the particle's linear momentum and r is the position vector from the origin. The time-derivative of this is: d L d t = r × d p d t + d r d t × p . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times {\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {p} .} This result can easily be proven by splitting
1476-648: Is a general proof for point particles, but it can be generalized to a system of point particles by applying the above proof to each of the point particles and then summing over all the point particles. Similarly, the proof can be generalized to a continuous mass by applying the above proof to each point within the mass, and then integrating over the entire mass. In physics , rotatum is the derivative of torque with respect to time P = d τ d t , {\displaystyle \mathbf {P} ={\frac {\mathrm {d} {\boldsymbol {\tau }}}{\mathrm {d} t}},} where τ
1558-459: Is an applied science used in several branches of engineering, including mechanical and chemical engineering. At its simplest, thermodynamics is the study of energy, its use and transformation through a system . Typically, engineering thermodynamics is concerned with changing energy from one form to another. As an example, automotive engines convert chemical energy ( enthalpy ) from the fuel into heat, and then into mechanical work that eventually turns
1640-437: Is commonly denoted by M . Just as a linear force is a push or a pull applied to a body, a torque can be thought of as a twist applied to an object with respect to a chosen point; for example, driving a screw uses torque, which is applied by the screwdriver rotating around its axis . A force of three newtons applied two metres from the fulcrum, for example, exerts the same torque as a force of one newton applied six metres from
1722-528: Is credited with the invention of the wheel by several, mainly old sources. However, some recent sources either suggest that it was invented independently in both Mesopotamia and Eastern Europe or credit prehistoric Eastern Europeans with the invention of the wheel The lever mechanism first appeared around 5,000 years ago in the Near East, where it was used in a simple balance scale , and to move large objects in ancient Egyptian technology . The lever
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#17327802355811804-746: Is one of the oldest and broadest of the engineering branches . Mechanical engineering requires an understanding of core areas including mechanics , dynamics , thermodynamics , materials science , design , structural analysis , and electricity . In addition to these core principles, mechanical engineers use tools such as computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), and product lifecycle management to design and analyze manufacturing plants , industrial equipment and machinery , heating and cooling systems , transport systems, motor vehicles , aircraft , watercraft , robotics , medical devices , weapons , and others. Mechanical engineering emerged as
1886-402: Is rotated by a vacuum actuator outside the manifold. T-VIS does not actually keep one of the intake valves from opening or seal off the port for one valve. The engine control unit (ECU) allows vacuum into the actuator by powering a solenoid valve when the engine rotation speed is low. At higher engine speeds (e.g. 4,200 rpm), vacuum is cut off and a spring inside the actuator causes
1968-425: Is the moment of inertia of the body and ω is its angular speed . Power is the work per unit time , given by P = τ ⋅ ω , {\displaystyle P={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},} where P is power, τ is torque, ω is the angular velocity , and ⋅ {\displaystyle \cdot } represents
2050-405: Is the newton-metre (N⋅m). For more on the units of torque, see § Units . The net torque on a body determines the rate of change of the body's angular momentum , τ = d L d t {\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}} where L is the angular momentum vector and t
2132-426: Is the means by which mechanical engineers design products and create instructions for manufacturing parts. A technical drawing can be a computer model or hand-drawn schematic showing all the dimensions necessary to manufacture a part, as well as assembly notes, a list of required materials, and other pertinent information. A U.S. mechanical engineer or skilled worker who creates technical drawings may be referred to as
2214-1748: Is time. For the motion of a point particle, L = I ω , {\displaystyle \mathbf {L} =I{\boldsymbol {\omega }},} where I = m r 2 {\textstyle I=mr^{2}} is the moment of inertia and ω is the orbital angular velocity pseudovector. It follows that τ n e t = I 1 ω 1 ˙ e 1 ^ + I 2 ω 2 ˙ e 2 ^ + I 3 ω 3 ˙ e 3 ^ + I 1 ω 1 d e 1 ^ d t + I 2 ω 2 d e 2 ^ d t + I 3 ω 3 d e 3 ^ d t = I ω ˙ + ω × ( I ω ) {\displaystyle {\boldsymbol {\tau }}_{\mathrm {net} }=I_{1}{\dot {\omega _{1}}}{\hat {\boldsymbol {e_{1}}}}+I_{2}{\dot {\omega _{2}}}{\hat {\boldsymbol {e_{2}}}}+I_{3}{\dot {\omega _{3}}}{\hat {\boldsymbol {e_{3}}}}+I_{1}\omega _{1}{\frac {d{\hat {\boldsymbol {e_{1}}}}}{dt}}+I_{2}\omega _{2}{\frac {d{\hat {\boldsymbol {e_{2}}}}}{dt}}+I_{3}\omega _{3}{\frac {d{\hat {\boldsymbol {e_{3}}}}}{dt}}=I{\boldsymbol {\dot {\omega }}}+{\boldsymbol {\omega }}\times (I{\boldsymbol {\omega }})} using
2296-451: Is torque, and θ 1 and θ 2 represent (respectively) the initial and final angular positions of the body. It follows from the work–energy principle that W also represents the change in the rotational kinetic energy E r of the body, given by E r = 1 2 I ω 2 , {\displaystyle E_{\mathrm {r} }={\tfrac {1}{2}}I\omega ^{2},} where I
2378-818: Is torque. This word is derived from the Latin word rotātus meaning 'to rotate', but the term rotatum is not universally recognized but is commonly used. There is not a universally accepted lexicon to indicate the successive derivatives of rotatum, even if sometimes various proposals have been made. Using the cross product definition of torque, an alternative expression for rotatum is: P = r × d F d t + d r d t × F . {\displaystyle \mathbf {P} =\mathbf {r} \times {\frac {\mathrm {d} \mathbf {F} }{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {r} }{\mathrm {d} t}}\times \mathbf {F} .} Because
2460-506: Is valid for any type of trajectory. In some simple cases like a rotating disc, where only the moment of inertia on rotating axis is, the rotational Newton's second law can be τ = I α {\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }}} where α = ω ˙ {\displaystyle {\boldsymbol {\alpha }}={\dot {\boldsymbol {\omega }}}} . The definition of angular momentum for
2542-624: Is zero because velocity and momentum are parallel, so the second term vanishes. Therefore, torque on a particle is equal to the first derivative of its angular momentum with respect to time. If multiple forces are applied, according Newton's second law it follows that d L d t = r × F n e t = τ n e t . {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} _{\mathrm {net} }={\boldsymbol {\tau }}_{\mathrm {net} }.} This
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2624-1049: The Accreditation Board for Engineering and Technology (ABET) to ensure similar course requirements and standards among universities. The ABET web site lists 302 accredited mechanical engineering programs as of 11 March 2014. Mechanical engineering programs in Canada are accredited by the Canadian Engineering Accreditation Board (CEAB), and most other countries offering engineering degrees have similar accreditation societies. In Australia , mechanical engineering degrees are awarded as Bachelor of Engineering (Mechanical) or similar nomenclature, although there are an increasing number of specialisations. The degree takes four years of full-time study to achieve. To ensure quality in engineering degrees, Engineers Australia accredits engineering degrees awarded by Australian universities in accordance with
2706-467: The Continent . The Dutch mathematician and physicist Christiaan Huygens invented the pendulum clock in 1657, which was the first reliable timekeeper for almost 300 years, and published a work dedicated to clock designs and the theory behind them. In England, Isaac Newton formulated Newton's Laws of Motion and developed the calculus , which would become the mathematical basis of physics. Newton
2788-522: The United States Military Academy in 1817, an institution now known as Norwich University in 1819, and Rensselaer Polytechnic Institute in 1825. Education in mechanical engineering has historically been based on a strong foundation in mathematics and science. Degrees in mechanical engineering are offered at various universities worldwide. Mechanical engineering programs typically take four to five years of study depending on
2870-427: The cross product of the displacement vector and the force vector. The direction of the torque can be determined by using the right hand grip rule : if the fingers of the right hand are curled from the direction of the lever arm to the direction of the force, then the thumb points in the direction of the torque. It follows that the torque vector is perpendicular to both the position and force vectors and defines
2952-505: The geometrical theorem of the same name) states that the resultant torques due to several forces applied to about a point is equal to the sum of the contributing torques: Mechanical engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science , to design , analyze, manufacture, and maintain mechanical systems . It
3034-414: The scalar product . Algebraically, the equation may be rearranged to compute torque for a given angular speed and power output. The power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied (this is equivalent to the linear case where the power injected by a force depends only on
3116-512: The "Principles and Practice" or PE (Practicing Engineer or Professional Engineer) exams. The requirements and steps of this process are set forth by the National Council of Examiners for Engineering and Surveying (NCEES), composed of engineering and land surveying licensing boards representing all U.S. states and territories. In the UK, current graduates require a BEng plus an appropriate master's degree or an integrated MEng degree,
3198-563: The 13th to 14th centuries. During the Islamic Golden Age (7th to 15th century), Muslim inventors made remarkable contributions in the field of mechanical technology. Al-Jazari , who was one of them, wrote his famous Book of Knowledge of Ingenious Mechanical Devices in 1206 and presented many mechanical designs. In the 17th century, important breakthroughs in the foundations of mechanical engineering occurred in England and
3280-472: The CD to the computer. Robotics is the application of mechatronics to create robots, which are often used in industry to perform tasks that are dangerous, unpleasant, or repetitive. These robots may be of any shape and size, but all are preprogrammed and interact physically with the world. To create a robot, an engineer typically employs kinematics (to determine the robot's range of motion) and mechanics (to determine
3362-465: The T-VIS open earlier than stock, because modifications that improve an engine's power output may do so by increasing airflow per engine revolution, resulting in a high airflow at a lower rpm. In addition to providing more air at higher engine speeds, the system also creates a swirl in the combustion chamber at lower rpms. The swirl makes for more efficient combustion, and is due to the asymmetric nature of
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3444-510: The U.S. workforce was $ 80,580. The median income was highest when working for the government ($ 92,030), and lowest in education ($ 57,090). In 2014, the total number of mechanical engineering jobs was projected to grow 5% over the next decade. As of 2009, the average starting salary was $ 58,800 with a bachelor's degree. The field of mechanical engineering can be thought of as a collection of many mechanical engineering science disciplines. Several of these subdisciplines which are typically taught at
3526-414: The U.S., for example, are required by ABET to show that their students can "work professionally in both thermal and mechanical systems areas." The specific courses required to graduate, however, may differ from program to program. Universities and institutes of technology will often combine multiple subjects into a single class or split a subject into multiple classes, depending on the faculty available and
3608-429: The UK, no such legislation exists; however, practically all certifying bodies maintain a code of ethics independent of legislation, that they expect all members to abide by or risk expulsion. The total number of engineers employed in the U.S. in 2015 was roughly 1.6 million. Of these, 278,340 were mechanical engineers (17.28%), the largest discipline by size. In 2012, the median annual income of mechanical engineers in
3690-595: The United Kingdom, Ireland, India and Zimbabwe), Chartered Professional Engineer (in Australia and New Zealand) or European Engineer (much of the European Union). In the U.S., to become a licensed Professional Engineer (PE), an engineer must pass the comprehensive FE (Fundamentals of Engineering) exam, work a minimum of 4 years as an Engineering Intern (EI) or Engineer-in-Training (EIT) , and pass
3772-566: The United States it is common for mechanical engineering students to complete one or more internships while studying, though this is not typically mandated by the university. Cooperative education is another option. Future work skills research puts demand on study components that feed student's creativity and innovation. Mechanical engineers research, design, develop, build, and test mechanical and thermal devices, including tools, engines, and machines. Mechanical engineers typically do
3854-721: The above expression for work, , gives W = ∫ s 1 s 2 F ⋅ d θ × r {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } The expression inside the integral is a scalar triple product F ⋅ d θ × r = r × F ⋅ d θ {\displaystyle \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} =\mathbf {r} \times \mathbf {F} \cdot \mathrm {d} {\boldsymbol {\theta }}} , but as per
3936-445: The airflow with one intake runner closed. Applications: Torque In physics and mechanics , torque is the rotational analogue of linear force . It is also referred to as the moment of force (also abbreviated to moment ). The symbol for torque is typically τ {\displaystyle {\boldsymbol {\tau }}} , the lowercase Greek letter tau . When being referred to as moment of force, it
4018-487: The butterfly valve to fully open. The idea behind the system is that in the lower engine speed band, the speed of the intake air will be increased because the intake runner cross section per cylinder is smaller. However, when engine speed increases, the second runner is opened, decreasing airflow speed, but increasing the airflow volume, better matching the engine's airflow needs at higher revolutions and improving top end power. With modified engines it may be desirable to have
4100-510: The core mechanical engineering curriculum, many mechanical engineering programs offer more specialized programs and classes, such as control systems , robotics, transport and logistics , cryogenics , fuel technology, automotive engineering , biomechanics , vibration, optics and others, if a separate department does not exist for these subjects. Most mechanical engineering programs also require varying amounts of research or community projects to gain practical problem-solving experience. In
4182-429: The crack is large enough to cause ultimate failure . Failure is not simply defined as when a part breaks, however; it is defined as when a part does not operate as intended. Some systems, such as the perforated top sections of some plastic bags, are designed to break. If these systems do not break, failure analysis might be employed to determine the cause. Structural analysis is often used by mechanical engineers after
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#17327802355814264-439: The definition of torque, and since the parameter of integration has been changed from linear displacement to angular displacement, the equation becomes W = ∫ θ 1 θ 2 τ ⋅ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}{\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}} If
4346-411: The derivative of a vector is d e i ^ d t = ω × e i ^ {\displaystyle {d{\boldsymbol {\hat {e_{i}}}} \over dt}={\boldsymbol {\omega }}\times {\boldsymbol {\hat {e_{i}}}}} This equation is the rotational analogue of Newton's second law for point particles, and
4428-428: The design or analysis phases of engineering. If the engineering project were the design of a vehicle, statics might be employed to design the frame of the vehicle, in order to evaluate where the stresses will be most intense. Dynamics might be used when designing the car's engine, to evaluate the forces in the pistons and cams as the engine cycles. Mechanics of materials might be used to choose appropriate materials for
4510-418: The entry point to academia . The Engineer's degree exists at a few institutions at an intermediate level between the master's degree and the doctorate. Standards set by each country's accreditation society are intended to provide uniformity in fundamental subject material, promote competence among graduating engineers, and to maintain confidence in the engineering profession as a whole. Engineering programs in
4592-537: The factory, robots have been employed in bomb disposal, space exploration , and many other fields. Robots are also sold for various residential applications, from recreation to domestic applications. Structural analysis is the branch of mechanical engineering (and also civil engineering) devoted to examining why and how objects fail and to fix the objects and their performance. Structural failures occur in two general modes: static failure, and fatigue failure. Static structural failure occurs when, upon being loaded (having
4674-471: The field of biomedical engineering , specifically with biomechanics , transport phenomena , biomechatronics , bionanotechnology , and modelling of biological systems. The application of mechanical engineering can be seen in the archives of various ancient and medieval societies. The six classic simple machines were known in the ancient Near East . The wedge and the inclined plane (ramp) were known since prehistoric times. Mesopotamian civilization
4756-607: The first factory for grinding machines in Chemnitz , Germany in 1848. In the United States, the American Society of Mechanical Engineers (ASME) was formed in 1880, becoming the third such professional engineering society, after the American Society of Civil Engineers (1852) and the American Institute of Mining Engineers (1871). The first schools in the United States to offer an engineering education were
4838-474: The following: Mechanical engineers design and oversee the manufacturing of many products ranging from medical devices to new batteries. They also design power-producing machines such as electric generators, internal combustion engines, and steam and gas turbines as well as power-using machines, such as refrigeration and air-conditioning systems. Like other engineers, mechanical engineers use computers to help create and analyze designs, run simulations and test how
4920-449: The formal name for the degree is "Mechanical Engineer", and the course work is based on five or six years of training. In Italy the course work is based on five years of education, and training, but in order to qualify as an Engineer one has to pass a state exam at the end of the course. In Greece, the coursework is based on a five-year curriculum. In the United States, most undergraduate mechanical engineering programs are accredited by
5002-493: The frame and engine. Fluid mechanics might be used to design a ventilation system for the vehicle (see HVAC ), or to design the intake system for the engine. Mechatronics is a combination of mechanics and electronics. It is an interdisciplinary branch of mechanical engineering, electrical engineering and software engineering that is concerned with integrating electrical and mechanical engineering to create hybrid automation systems. In this way, machines can be automated through
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#17327802355815084-534: The fulcrum. The term torque (from Latin torquēre , 'to twist') is said to have been suggested by James Thomson and appeared in print in April, 1884. Usage is attested the same year by Silvanus P. Thompson in the first edition of Dynamo-Electric Machinery . Thompson motivates the term as follows: Just as the Newtonian definition of force is that which produces or tends to produce motion (along
5166-562: The global Washington Accord . Before the degree can be awarded, the student must complete at least 3 months of on the job work experience in an engineering firm. Similar systems are also present in South Africa and are overseen by the Engineering Council of South Africa (ECSA). In India , to become an engineer, one needs to have an engineering degree like a B.Tech. or B.E., have a diploma in engineering, or by completing
5248-568: The infinitesimal linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } is related to a corresponding angular displacement d θ {\displaystyle \mathrm {d} {\boldsymbol {\theta }}} and the radius vector r {\displaystyle \mathbf {r} } as d s = d θ × r {\displaystyle \mathrm {d} \mathbf {s} =\mathrm {d} {\boldsymbol {\theta }}\times \mathbf {r} } Substitution in
5330-586: The instantaneous speed – not on the resulting acceleration, if any). The work done by a variable force acting over a finite linear displacement s {\displaystyle s} is given by integrating the force with respect to an elemental linear displacement d s {\displaystyle \mathrm {d} \mathbf {s} } W = ∫ s 1 s 2 F ⋅ d s {\displaystyle W=\int _{s_{1}}^{s_{2}}\mathbf {F} \cdot \mathrm {d} \mathbf {s} } However,
5412-452: The place and university and result in a Bachelor of Engineering (B.Eng. or B.E.), Bachelor of Science (B.Sc. or B.S.), Bachelor of Science Engineering (B.Sc.Eng.), Bachelor of Technology (B.Tech.), Bachelor of Mechanical Engineering (B.M.E.), or Bachelor of Applied Science (B.A.Sc.) degree, in or with emphasis in mechanical engineering. In Spain, Portugal and most of South America, where neither B.S. nor B.Tech. programs have been adopted,
5494-405: The plane in which the two vectors lie. The resulting torque vector direction is determined by the right-hand rule. Therefore any force directed parallel to the particle's position vector does not produce a torque. The magnitude of torque applied to a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to
5576-436: The point of force application, and the angle between the force and lever arm vectors. In symbols: τ = r × F ⟹ τ = r F ⊥ = r F sin θ {\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \implies \tau =rF_{\perp }=rF\sin \theta } where The SI unit for torque
5658-528: The rate of change of force is yank Y {\textstyle \mathbf {Y} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , the expression can be further simplified to: P = r × Y + v × F . {\displaystyle \mathbf {P} =\mathbf {r} \times \mathbf {Y} +\mathbf {v} \times \mathbf {F} .} The law of conservation of energy can also be used to understand torque. If
5740-615: The seventh century BC in Meroe . Kushite sundials applied mathematics in the form of advanced trigonometry. The earliest practical water-powered machines, the water wheel and watermill , first appeared in the Persian Empire , in what are now Iraq and Iran, by the early 4th century BC. In ancient Greece , the works of Archimedes (287–212 BC) influenced mechanics in the Western tradition. The geared Antikythera mechanisms
5822-513: The stresses within the robot). Robots are used extensively in industrial automation engineering. They allow businesses to save money on labor, perform tasks that are either too dangerous or too precise for humans to perform them economically, and to ensure better quality. Many companies employ assembly lines of robots, especially in Automotive Industries and some factories are so robotized that they can run by themselves . Outside
5904-525: The subject of graduate studies or on-the-job training than undergraduate research. Several specialized subdisciplines are discussed in this section. Mechanics is, in the most general sense, the study of forces and their effect upon matter . Typically, engineering mechanics is used to analyze and predict the acceleration and deformation (both elastic and plastic ) of objects under known forces (also called loads) or stresses . Subdisciplines of mechanics include Mechanical engineers typically use mechanics in
5986-875: The torque and the angular displacement are in the same direction, then the scalar product reduces to a product of magnitudes; i.e., τ ⋅ d θ = | τ | | d θ | cos 0 = τ d θ {\displaystyle {\boldsymbol {\tau }}\cdot \mathrm {d} {\boldsymbol {\theta }}=\left|{\boldsymbol {\tau }}\right|\left|\mathrm {d} {\boldsymbol {\theta }}\right|\cos 0=\tau \,\mathrm {d} \theta } giving W = ∫ θ 1 θ 2 τ d θ {\displaystyle W=\int _{\theta _{1}}^{\theta _{2}}\tau \,\mathrm {d} \theta } The principle of moments, also known as Varignon's theorem (not to be confused with
6068-487: The undergraduate level are listed below, with a brief explanation and the most common application of each. Some of these subdisciplines are unique to mechanical engineering, while others are a combination of mechanical engineering and one or more other disciplines. Most work that a mechanical engineer does uses skills and techniques from several of these subdisciplines, as well as specialized subdisciplines. Specialized subdisciplines, as used in this article, are more likely to be
6150-631: The university's major area(s) of research. The fundamental subjects required for mechanical engineering usually include: Mechanical engineers are also expected to understand and be able to apply basic concepts from chemistry, physics, tribology , chemical engineering , civil engineering , and electrical engineering . All mechanical engineering programs include multiple semesters of mathematical classes including calculus, and advanced mathematical concepts including differential equations , partial differential equations , linear algebra , differential geometry , and statistics , among others. In addition to
6232-404: The use of electric motors , servo-mechanisms , and other electrical systems in conjunction with special software. A common example of a mechatronics system is a CD-ROM drive. Mechanical systems open and close the drive, spin the CD and move the laser, while an optical system reads the data on the CD and converts it to bits . Integrated software controls the process and communicates the contents of
6314-733: The vectors into components and applying the product rule . But because the rate of change of linear momentum is force F {\textstyle \mathbf {F} } and the rate of change of position is velocity v {\textstyle \mathbf {v} } , d L d t = r × F + v × p {\displaystyle {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=\mathbf {r} \times \mathbf {F} +\mathbf {v} \times \mathbf {p} } The cross product of momentum p {\displaystyle \mathbf {p} } with its associated velocity v {\displaystyle \mathbf {v} }
6396-410: The wheels. Thermodynamics principles are used by mechanical engineers in the fields of heat transfer , thermofluids , and energy conversion . Mechanical engineers use thermo-science to design engines and power plants , heating, ventilation, and air-conditioning (HVAC) systems, heat exchangers , heat sinks , radiators , refrigeration , insulation , and others. Drafting or technical drawing
6478-568: The world's first known endless power-transmitting chain drive . The cotton gin was invented in India by the 6th century AD, and the spinning wheel was invented in the Islamic world by the early 11th century, Dual-roller gins appeared in India and China between the 12th and 14th centuries. The worm gear roller gin appeared in the Indian subcontinent during the early Delhi Sultanate era of
6560-697: Was also used in the shadoof water-lifting device, the first crane machine, which appeared in Mesopotamia circa 3000 BC. The earliest evidence of pulleys date back to Mesopotamia in the early 2nd millennium BC. The Sakia was developed in the Kingdom of Kush during the 4th century BC. It relied on animal power reducing the tow on the requirement of human energy. Reservoirs in the form of Hafirs were developed in Kush to store water and boost irrigation. Bloomeries and blast furnaces were developed during
6642-582: Was an Analog computer invented around the 2nd century BC. In Roman Egypt , Heron of Alexandria (c. 10–70 AD) created the first steam-powered device ( Aeolipile ). In China , Zhang Heng (78–139 AD) improved a water clock and invented a seismometer , and Ma Jun (200–265 AD) invented a chariot with differential gears. The medieval Chinese horologist and engineer Su Song (1020–1101 AD) incorporated an escapement mechanism into his astronomical clock tower two centuries before escapement devices were found in medieval European clocks. He also invented
6724-510: Was reluctant to publish his works for years, but he was finally persuaded to do so by his colleagues, such as Edmond Halley . Gottfried Wilhelm Leibniz , who earlier designed a mechanical calculator , is also credited with developing the calculus during the same time period. During the early 19th century Industrial Revolution, machine tools were developed in England, Germany , and Scotland . This allowed mechanical engineering to develop as
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