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

This assembly is called a linkage. Reverse motion 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. Motion at right angles Linear motion to rotary motion

Reverse motion linkages Off-center fixed pivot 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

Lever Graphic Symbols 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) 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. Velocity ratio = Number of teeth on driven sprocket 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 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 Velocity ratio Prove ? 2R (R-r) 2R (R-r)

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 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. Pinion Wheel

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 ?

Velocity ratio (gear ratio) 60 revs / min 20 teeth driven gear 40 teeth driver gear Velocity ratio (gear ratio) Mechanical advantage number of teeth on driven gear number of teeth on the driver gear Load torque Effort torque F x R F x r = 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 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.

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

number of teeth on wormwheel number of teeth on 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 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.

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

Applications: