Engineering System Mechanisms Basic Mechanisms I Content Lever

Engineering System : Mechanisms Basic Mechanisms ( I )

Content • • • Lever (槓桿 ) Linkage (聯動裝置 ) Pulley (滑輪) Sprocket (鏈輪) Gear (齒輪)

Lever (槓桿 ) • Lever is a rigid rod pivoted about a fixed axis called a fulcrum. • A lever can produce a small output motion from a large input motion. • There are three types of lever. Each class has the fulcrum, effort and load arranged in different way. – Class 1 lever – Class 2 lever – Class 3 lever

• Class 1 – With a class 1 lever the fulcrum is in the middle. The effort is on one side and the load is on the other.

• Class 2 – The fulcrum is at one end, the effort is at the other end and the load is in the middle. – A class two lever allows a large load to be lifted by a smaller effort.

• Class 3 – With a class 3 lever, the fulcrum is at one end, the load is at the other and the effort is in the middle. – A class 3 lever allows a small load to be lifted by a larger effort.

• Bell Crank Lever – The bell crank lever is a right-angle Class 1 Lever – The input motion is transmitted through a right angle to give an output motion. – Application: • The altimeter

• Toggles (肘節機件 ) =lever + link – The mechanisms consists of two links on a common pivot. – The free end of one link is pivoted to a fixed surface. – The free end of the second lever is constrained to move in a straight line. – By applying a horizontal effort to the common pivot, the lower end of the toggle mechanisms is pushed downwards.

Linkage (聯動裝置 ) A “Black Box” Mechanisms • It is often convenient to think of a mechanism as a “black box” • It is not important what goes on inside the box, just what needs to go into it to produce the output you want. • Linkage is one of such “Black Box” A “black box” mechanism

• The system inside the “black box” alters the input motion in some desire way. • One type of “black box” function is created by an assembly of levers which transforms and transmits an input. • This assembly is called a linkage. Reverse motion Motion at right angles Linear motion to rotary motion

• Reverse motion linkages Center fixed pivot Off-center fixed pivot

• Push-pull linkage – To achieve an output motion in the same direction as the input motion. – Two fixed pivots and an extra link arm are necessary.

• An equalising linkage – To divide the applied input force along two output links.

• Parallel motion linkage Parallel hinges on a tool box

• Graphic Symbols Lever – Complex mechanisms and linkages consist of basically simple devices. – The functioning of a mechanical system can be easily illustrated by the use of graphic symbols for levers, pivots and springs. Pivot lever Fixed pivot Slide

A mechanical typewriter mechanism The type writer mechanism using graphic symbols

Pulley (滑輪) & Sprocket (鏈輪) • Pulley – A wheel with a grooved rim. – To transmit the rotary motion from one shaft to another when the shafts are parallel.

• A crossed belt is used between two pulleys when the parallel shaft are required to turn in opposite directions. Pulleys offset on shafts

• Input & Output velocities of rotation – The pulley on the motor is called the driver pulley – The pulley on the machine being driven by the belt is called a driven pulley. – The velocity of rotation of the machine shaft is determined by • The velocity of the driving motor • The size of the pulleys Question: What is the velocity of the driven pulley? Ans: 200

• Pulley applications – The main functions of pulley are to transmit motion and torque from an engine to a machine. • e. g. washing machine, spin drier – Provide a range of shaft speed • e. g. stepped cone pulley for drilling machine

• To avoid slip in a pulley and belt system by means of a jockey pulley. – An additional pulley which keeps the maximum amount of belt in contact with the driver and driven pulley. – Spring loaded

• Is belt slipping bad? – If a machine tool jams or seizes and the belt slips on the pulleys, the driving motor is unlikely to be overloaded and damaged. – In machines where positive drive is essential and no slip between and pulleys can be accepted, a toothed belt and pulley is used.

Sprocket (鏈輪) • Sprocket is a toothed belt and used with a chain which consists of many loosely jointed links.

• The links of a chain require equal spacing of equal teeth on the driver and driven sprockets. • Velocity ratio is determined by the number of teeth on each sprocket. Number of teeth on driven sprocket Velocity ratio = Number of teeth on driver sprocket

Pulley and lifting devices • Pulley is a form of Class 1 lever • When a single pulley is used, its only function is to change the direction of the tension force in the rope. • The fixed pulley and movable pulley are often combined as lifting device.

• What is the mechanical advantages of the following systems?

Question • What is the mechanical advantages of the following system? • Draw a pulley system similar to this system but having one more rope and one more pulley. What is the mechanical advantage and velocity ratio of the new system?

Wheel & Axle • The wheel and axle provides a mechanical advantage by use of a large radius wheel and a smaller radius axle. – e. g. shaft and wheel of a motor car, bicycle wheel and axle, car steeling wheel

• The mechanical advantage = – R : the radius of effort wheel – r : the radius of load axle • What is the velocity ratio? R r

• Weston differential pulley – It consists of a continuous rope or chain round two upper pulleys and one lower movable pulley. – Two upper pulleys have different diameters but they are rigidly connected together. – Special advantage : effort will move the load but he load cannot move the effort.

• Mechanical advantage 2 R (R-r) • Velocity ratio 2 R (R-r) • Prove ?

Gear (齒輪) • • • Spur gear Gear train Compound gear train Revel gears Crossed helical gears Worm & worm wheel Parallel helical gear Spiral bevel gears Rack & pinion

• Spur gear – When two spur gears of different sizes mesh together, the larger gear is called a wheel, and the smaller one is called a pinion. Wheel Pinion Spur gear

• Graphic symbols – A graphic symbol of two concentric circles is used to represent a gear. – The outer circle is the tip circle and represents a circle on which lie the tips of the gear teeth. – The inner circle is the root circle and represents a circle on which lie the bottoms of the spaces between the teeth.

• Transmission of force Torque : the turning moment F x r – When two gear wheels the same size are meshed, they act as a simple torque transmitter – When two gears with different sizes are meshed, they act as torque converter torque vs velocity ?

60 revs / min • Velocity ratio (gear ratio) number of teeth on driven gear number of teeth on the driver gear • Mechanical advantage Load torque Effort torque = Fx. R Fxr 20 teeth driven gear 40 teeth driver gear What is the velocity of the driven gear? Ans : 120

• Gear train – Consist of two or more meshed gear. – Simple gear train has two gears rotates in opposite direction. – The intermediate gear between the driver gear and the driven gear is called an idler gear. – The idler gear only serves to keep the driver and driven gear rotating in the same direction.

• Compound gear train – The gear train has a driver gear and a driven gear, but he intermediate gears are fixed together on one common shaft. Compound gear

• Tumbler reverse gear mechanism – Two idler gears are used to enable the spindle to rotate the first driver gear of the gear train in a forward or reverse direction. forward neutral reverse

Gearbox design • Transmission through a right angle – – Bevel gears Crossed helical gears Wormwheel Other special gears and applications

• Bevel gears – Having teeth cut on a cone instead of a cylinder blank. – They are used in pairs to transmit rotary motion and torque where the bevel gear shafts are right angles to each other.

• Crossed helical gears – The teethes of a helical gear are inclined at angle to the axis of rotation of the gear. – Helical gears are smoother running than spur gears and are more suitable for rotation at high velocity.

• Wormwheel – A gear which has one tooth is called a worm. The tooth is in the form of a screw thread. – The wormwheel is helical gear with teeth inclined so that they can engage with the thread-like worm. – Wormwheel meshes with the worm

– The mechanisms locks if the wormwheel tries to drive the worm. – Worm mechanisms are very quiet running. – Gear ratio of a meshed worm & wormwheel number of teeth on worm = number or the teeth on the wormwheel Why

• Special gears & Applications – – – Parallel helical gears Double helical gears Spiral bevel gears Face cut gears Internal gears Rack & pinion

• Parallel helical gears – Parallel helical gears have their teeth inclined at a small angle to their axis of rotation. – The gears can move along a splined (grooved) shaft, although they rotate with the shaft. – For applications that require very quiet and smooth running at high rotational velocity.

• Double helical gears – Give an efficient transfer of torque and smooth motion at very high rotational velocities.

• Spiral bevel gears – To transmit quietly and smoothly a large torque through a right angle at high velocities. – Having teeth cut in a helix spiral form on the surface of a cone. – Quieter running than straight bevel gears and have a longer life – Used in motorcar rear axle gearboxes.

• Face cut gears & internal gears – Cut gear teeth on the face of a gear wheel. – Gear teach can be cut on the inside of a gear ring. • Better load-carrying capacity than external spur gears. • Safer in used because the teeth are guarded.

• Rack & pinion – Converting rotary motion to linear motion – A round spur gear, the pinion, meshes with a spur gear which has teeth set in a straight line, the rack.

• The rack & pinion can transform rotary motion into linear motion and vice versa in three ways: – Rotation of the pinion about a fixed center causes the rack to move in a straight line – Movement of the rack in a straight line causes the pinion to rotate about a fixed center – If the rack is fixed and the pinion rotates, then the pinion’s center move in a straight line taking the pinion with it.

Rack 200 teeth/meter Exercise What is distance moved by the rack for every revolution of the pinion? Ans : 100 mm Pinion 20 teeth

• Applications: