Mechanics Quiz: Kinematics and Dynamics of Machines

Mechanics: Study of Motion, Time, and Force

• Mechanics is a branch of scientific analysis that deals with motion, time, and force.
• Kinematics is the study of motion without considering the forces that produce that motion.
• Kinematics of machines deals with the study of the relative motion of machine parts.
• It involves the study of position, displacement, velocity, and acceleration of machine parts.

Plane Motion

• A body has plane motion if all its points move in planes parallel to some reference plane.
• A body with plane motion will have only three degrees of freedom.
• Plane motion can be of three types: translation, rotation, and combination of translation and rotation.

Kinematic Link (or Element)

• A machine part or a component of a mechanism is called a kinematic link or simply a link.
• A link is assumed to be completely rigid and does not suffer any deformation.
• Types of links are:
  • Binary link: connected to other links at two points.
  • Ternary link: connected to other links at three points.
  • Quaternary link: connected to other links at four points.

Kinematic Chain

• A mechanism is a kinematic chain with one of the links fixed.
• A simple mechanism is a kinematic chain with four links.
• A compound mechanism is a kinematic chain with more than four links.

Kinematic Pair

• Two links or elements of a machine that are in contact with each other are said to form a pair.
• If the relative motion between them is completely or successfully constrained, the pair is known as a kinematic pair.
• Classification of kinematic pairs:
  • Based on nature of contact: lower pair, higher pair.
  • Based on relative motion: sliding pair, turning pair, cylindrical pair, rolling pair, spherical pair, helical pair.
  • Based on nature of mechanical constraint: closed pair, unclosed or force-closed pair.

Degrees of Freedom

• Degrees of freedom (DOF) is the number of independent coordinates required to describe the position of a body in space.
• In a kinematic pair, the links may lose some of the six degrees of freedom.
• Kutzbach criterion for the mobility of a planar mechanism: F = 3(n-1) - 2l - h, where F is the degree of freedom, n is the number of links, l is the number of lower joints, and h is the number of higher pairs.

Inversion of Mechanism

• Inversion of a mechanism is obtained by fixing different links of the same kinematic chain.
• Inversions of a four-bar chain: crank-rocker mechanism, double crank mechanism, double rocker mechanism.

Coupler Curves

• The link connecting the driving crank with the follower crank in a four-bar linkage is called the coupler.
• During the motion of the mechanism, any point attached to the coupler generates some path with respect to the fixed link, which is called the coupler curve.

Quick Return Motion Mechanisms

• Quick return motion mechanisms are used in machine tools to give the reciprocating cutting tool a slow cutting stroke and a quick return stroke.
• Examples of quick return motion mechanisms: Whitworth quick return motion mechanism, crank and slotted lever quick return motion mechanism.

Velocity and Acceleration Analysis

• Velocity analysis is important for determining the acceleration of points in the mechanisms.
• Kinematics deals with the study of relative motion between the various parts of the machines.
• Displacement, velocity, and acceleration are key concepts in kinematics.
• Analysis can be carried out by graphical method as well as analytical method.

Kinematic Synthesis

• Kinematic synthesis, also known as mechanism synthesis, determines the size and configuration of mechanisms to achieve a desired performance.
• It involves combining parts to form a whole, creating something new, and converting motion ideas into hardware.
• Machines use chemical and electric power to manufacture, transport, and process items, and kinematic synthesis is used to design the elements that achieve required output forces and movement for a given input.

Linkages

• Linkages are the basic building blocks of all mechanisms.
• They are made up of links and joints.
• Links are rigid members with nodes (attachment points).
• Joints are connections between two or more links that allow motion.
• Joints can be classified in several ways, including:
  • Type of contact between elements (line, point, or surface)
  • Number of degrees of freedom allowed
  • Type of physical closure (force or form closed)
  • Number of links joined (order of the joint)

Dynamic Force Analysis

• D'Alembert's principle states that the reverse-effective forces and torques, and the external forces and torques on a body, together give statical equilibrium.
• The principle can be used to derive the inertia force and inertia torque equations.
• Inertia force (Fi) is proportional to the mass of the body and its acceleration.
• Inertia torque (Ci) is a pure torque or couple.

Equivalent Offset Inertia Force

• The equivalent offset inertia force is a single force that accounts for both translational inertia and rotational inertia.
• It is used for graphical plane force analysis.
• The force is equivalent to the combination of a force and a torque.
• The magnitude of the force is |maG|.
• The direction of the force is opposite to that of acceleration a.
• The perpendicular offset distance from the center of mass to the line of action of the force.

Dynamic Analysis of Mechanisms

• Dynamic analysis of a four-bar linkage illustrates the ideas presented in the chapter.
• The analysis of a slider-crank mechanism demonstrates the importance of considering dynamic forces in design.

Free Body Diagram

• A free body diagram helps in understanding and solving static and dynamic problems involving forces.
• It includes all forces acting on a given object without the other object in the system.
• The diagram is used to represent forces by arrows in the direction of the force.
• Examples of free body diagrams include a book on a table, a suspended block, and a block on a floor with an acting force.

Kinematic Synthesis

• Kinematic synthesis, also known as mechanism synthesis, determines the size and configuration of mechanisms to achieve a desired performance.
• It involves combining parts to form a whole, creating something new, and converting motion ideas into hardware.
• Machines use chemical and electric power to manufacture, transport, and process items, and kinematic synthesis is used to design the elements that achieve required output forces and movement for a given input.

Linkages

• Linkages are the basic building blocks of all mechanisms.
• They are made up of links and joints.
• Links are rigid members with nodes (attachment points).
• Joints are connections between two or more links that allow motion.
• Joints can be classified in several ways, including:
  • Type of contact between elements (line, point, or surface)
  • Number of degrees of freedom allowed
  • Type of physical closure (force or form closed)
  • Number of links joined (order of the joint)

Dynamic Force Analysis

• D'Alembert's principle states that the reverse-effective forces and torques, and the external forces and torques on a body, together give statical equilibrium.
• The principle can be used to derive the inertia force and inertia torque equations.
• Inertia force (Fi) is proportional to the mass of the body and its acceleration.
• Inertia torque (Ci) is a pure torque or couple.

Equivalent Offset Inertia Force

• The equivalent offset inertia force is a single force that accounts for both translational inertia and rotational inertia.
• It is used for graphical plane force analysis.
• The force is equivalent to the combination of a force and a torque.
• The magnitude of the force is |maG|.
• The direction of the force is opposite to that of acceleration a.
• The perpendicular offset distance from the center of mass to the line of action of the force.

Dynamic Analysis of Mechanisms

• Dynamic analysis of a four-bar linkage illustrates the ideas presented in the chapter.
• The analysis of a slider-crank mechanism demonstrates the importance of considering dynamic forces in design.

Free Body Diagram

• A free body diagram helps in understanding and solving static and dynamic problems involving forces.
• It includes all forces acting on a given object without the other object in the system.
• The diagram is used to represent forces by arrows in the direction of the force.
• Examples of free body diagrams include a book on a table, a suspended block, and a block on a floor with an acting force.

Kinematic Synthesis

• Kinematic synthesis, also known as mechanism synthesis, determines the size and configuration of mechanisms to achieve a desired performance.
• It involves combining parts to form a whole, creating something new, and converting motion ideas into hardware.
• Machines use chemical and electric power to manufacture, transport, and process items, and kinematic synthesis is used to design the elements that achieve required output forces and movement for a given input.

Linkages

• Linkages are the basic building blocks of all mechanisms.
• They are made up of links and joints.
• Links are rigid members with nodes (attachment points).
• Joints are connections between two or more links that allow motion.
• Joints can be classified in several ways, including:
  • Type of contact between elements (line, point, or surface)
  • Number of degrees of freedom allowed
  • Type of physical closure (force or form closed)
  • Number of links joined (order of the joint)

Dynamic Force Analysis

• D'Alembert's principle states that the reverse-effective forces and torques, and the external forces and torques on a body, together give statical equilibrium.
• The principle can be used to derive the inertia force and inertia torque equations.
• Inertia force (Fi) is proportional to the mass of the body and its acceleration.
• Inertia torque (Ci) is a pure torque or couple.

Equivalent Offset Inertia Force

• The equivalent offset inertia force is a single force that accounts for both translational inertia and rotational inertia.
• It is used for graphical plane force analysis.
• The force is equivalent to the combination of a force and a torque.
• The magnitude of the force is |maG|.
• The direction of the force is opposite to that of acceleration a.
• The perpendicular offset distance from the center of mass to the line of action of the force.

Dynamic Analysis of Mechanisms

• Dynamic analysis of a four-bar linkage illustrates the ideas presented in the chapter.
• The analysis of a slider-crank mechanism demonstrates the importance of considering dynamic forces in design.

Free Body Diagram

• A free body diagram helps in understanding and solving static and dynamic problems involving forces.
• It includes all forces acting on a given object without the other object in the system.
• The diagram is used to represent forces by arrows in the direction of the force.
• Examples of free body diagrams include a book on a table, a suspended block, and a block on a floor with an acting force.

Cam and Follower

• A cam is a mechanical device used to transmit motion to a follower by direct contact.
• The cam and follower have line contact and constitute a higher pair.
• The cam normally rotates at uniform speed, while the follower translates or oscillates according to the shape of the cam.

Applications of Cams

• Widely used in operating inlet and exhaust valves of Internal Combustion Engines
• Used in automatic attachment of machineries, paper cutting machines, spinning and weaving textile machineries, and feed mechanism of automatic lathes

Types of Followers

• Based on surface in contact:
  • Knife edge follower
  • Roller follower
  • Flat faced follower
  • Spherical follower
• Based on type of motion:
  • Oscillating follower
  • Translating follower

Classification of Cams

• Based on physical shape:
  • Disk or plate cam
  • Cylindrical cam
  • Translating cam

Terms Used in Radial Cams

• Pressure angle: the angle between the direction of the follower motion and a normal to the pitch curve
• Base circle: the smallest circle that can be drawn to the cam profile
• Trace point: the reference point on the follower used to generate the pitch curve
• Pitch point: a point on the pitch curve having the maximum pressure angle
• Pitch circle: a circle drawn from the centre of the cam through the pitch points
• Pitch curve: the curve generated by the trace point as the follower moves relative to the cam
• Prime circle: the smallest circle that can be drawn from the centre of the cam and tangent to the point

Motion of the Follower

• Cam follower systems are designed to achieve a desired oscillatory motion
• Appropriate displacement patterns are to be selected for this purpose, before designing the cam surface
• Some of the standard follower motions are:
  • Uniform velocity
  • Modified uniform velocity
  • Uniform acceleration and deceleration
  • Simple harmonic motion

Displacement Diagrams

• Displacement diagrams plot the motion of the follower against the angular displacement of the cam
• From the displacement diagram, velocity and acceleration of the follower can also be plotted for different angular displacements of the cam
• Displacement diagrams are basic requirements for the construction of cam profiles

Cam and Follower

• A cam is a mechanical device used to transmit motion to a follower by direct contact.
• The cam and follower have line contact and constitute a higher pair.
• The cam normally rotates at uniform speed, while the follower translates or oscillates according to the shape of the cam.

Applications of Cams

• Widely used in operating inlet and exhaust valves of Internal Combustion Engines
• Used in automatic attachment of machineries, paper cutting machines, spinning and weaving textile machineries, and feed mechanism of automatic lathes

Types of Followers

• Based on surface in contact:
  • Knife edge follower
  • Roller follower
  • Flat faced follower
  • Spherical follower
• Based on type of motion:
  • Oscillating follower
  • Translating follower

Classification of Cams

• Based on physical shape:
  • Disk or plate cam
  • Cylindrical cam
  • Translating cam

Terms Used in Radial Cams

• Pressure angle: the angle between the direction of the follower motion and a normal to the pitch curve
• Base circle: the smallest circle that can be drawn to the cam profile
• Trace point: the reference point on the follower used to generate the pitch curve
• Pitch point: a point on the pitch curve having the maximum pressure angle
• Pitch circle: a circle drawn from the centre of the cam through the pitch points
• Pitch curve: the curve generated by the trace point as the follower moves relative to the cam
• Prime circle: the smallest circle that can be drawn from the centre of the cam and tangent to the point

Motion of the Follower

• Cam follower systems are designed to achieve a desired oscillatory motion
• Appropriate displacement patterns are to be selected for this purpose, before designing the cam surface
• Some of the standard follower motions are:
  • Uniform velocity
  • Modified uniform velocity
  • Uniform acceleration and deceleration
  • Simple harmonic motion

Displacement Diagrams

• Displacement diagrams plot the motion of the follower against the angular displacement of the cam
• From the displacement diagram, velocity and acceleration of the follower can also be plotted for different angular displacements of the cam
• Displacement diagrams are basic requirements for the construction of cam profiles

Cam and Follower

• A cam is a mechanical device used to transmit motion to a follower by direct contact.
• The cam and follower have line contact and constitute a higher pair.
• The cam normally rotates at uniform speed, while the follower translates or oscillates according to the shape of the cam.

Applications of Cams

• Widely used in operating inlet and exhaust valves of Internal Combustion Engines
• Used in automatic attachment of machineries, paper cutting machines, spinning and weaving textile machineries, and feed mechanism of automatic lathes

Types of Followers

• Based on surface in contact:
  • Knife edge follower
  • Roller follower
  • Flat faced follower
  • Spherical follower
• Based on type of motion:
  • Oscillating follower
  • Translating follower

Classification of Cams

• Based on physical shape:
  • Disk or plate cam
  • Cylindrical cam
  • Translating cam

Terms Used in Radial Cams

• Pressure angle: the angle between the direction of the follower motion and a normal to the pitch curve
• Base circle: the smallest circle that can be drawn to the cam profile
• Trace point: the reference point on the follower used to generate the pitch curve
• Pitch point: a point on the pitch curve having the maximum pressure angle
• Pitch circle: a circle drawn from the centre of the cam through the pitch points
• Pitch curve: the curve generated by the trace point as the follower moves relative to the cam
• Prime circle: the smallest circle that can be drawn from the centre of the cam and tangent to the point

Motion of the Follower

• Cam follower systems are designed to achieve a desired oscillatory motion
• Appropriate displacement patterns are to be selected for this purpose, before designing the cam surface
• Some of the standard follower motions are:
  • Uniform velocity
  • Modified uniform velocity
  • Uniform acceleration and deceleration
  • Simple harmonic motion

Displacement Diagrams

• Displacement diagrams plot the motion of the follower against the angular displacement of the cam
• From the displacement diagram, velocity and acceleration of the follower can also be plotted for different angular displacements of the cam
• Displacement diagrams are basic requirements for the construction of cam profiles

Belt Drives

• A belt is a looped strip of flexible material used to mechanically link two or more rotating shafts, offering smooth transmission of power between shafts at a considerable distance.
• Belt drives are used to efficiently transmit power or to track relative movement.
• There are two types of belt drives: open belt drives and crossed belt drives.

Open Belt Drives

• Used to rotate the driven pulley in the same direction as the driving pulley.
• Power transmission results in one side of the pulley being more tightened than the other side.
• In horizontal drives, the tightened side is always kept on the lower side of two pulleys.

Crossed Belt Drives

• Used to rotate the driven pulley in the opposite direction of the driving pulley.
• Higher wrap values enable more power transmission, but bending and wear of the belt are important concerns.

Advantages of Belt Drives

• Simple and economical
• Don't require parallel shafts
• Provided with overload and jam protection
• Noise and vibration are damped out, increasing machinery life
• Lubrication-free and require less maintenance cost
• Highly efficient (up to 98%, usually 95%)
• Economical when the distance between shafts is very large

Disadvantages of Belt Drives

• Angular velocity ratio is not necessarily constant or equal to the ratio of pulley diameters due to slipping and stretching
• Heat buildup occurs
• Speed is limited to usually 35 meters per second
• Power transmission is limited to 370 kilowatts
• Operating temperatures are usually restricted to -35 to 85°C
• Adjustment of center distance or use of an idler pulley is necessary for wearing and stretching compensation

Clutches

• A mechanical device that engages and disengages power transmission from the driving shaft to the driven shaft
• One shaft is connected to an engine or power unit, while the other shaft provides output power for the work

Types of Clutches

• Friction clutch
  • Single plate clutch
  • Multiplate clutch
    • Wet
    • Dry
• Cone clutch
  • External
  • Internal
• Centrifugal clutch
• Semi-centrifugal clutch
• Conical spring clutch or Diaphragm clutch
  • Tapered finger type
  • Crown spring type
• Positive clutch
  • Dog clutch
• Spline clutch
• Hydraulic clutch
• Electromagnetic clutch
• Vacuum clutch
• Overrunning clutch or freewheel unit

Single Clutch Plate

• One of the most commonly used types of clutches in light vehicles
• Consists of a clutch plate, friction plate, pressure plate, flywheel, bearings, clutch spring, and not-bolts arrangement
• The clutch plate is a thin metallic disc with friction surfaces on both sides
• Working:
  • When the clutch pedal is pressed, the springs get compressed, and the pressure plate moves backward
  • The clutch plate becomes free between the pressure plate and flywheel, disengaging the clutch
  • The flywheel continues to rotate as long as the engine is running, and the clutch shaft speed reduces slowly and then stops rotating

Multiplate Clutch

• Uses multiple clutches to make frictional contact with a flywheel of the engine
• Increases the capacity of the clutch to transmit torque
• Working principle is the same as the single-plate clutch
• Used in heavy commercial vehicles, racing cars, and motorcycles for transmitting high torque
• Can be dry or wet, with wet clutches commonly used in automatic transmissions

Cone Clutch

• Uses two conical surfaces to transmit torque by friction
• The engine shaft consists of a female cone and a male cone
• The male cone is mounted on the splined clutch shaft to slide on it
• Working:
  • When the clutch is engaged, the friction surfaces of the male cone are in contact with the female cone
  • When the clutch pedal is pressed, the male cone slides towards the spring force, and the clutch is disengaged

Centrifugal Clutch

• Uses centrifugal force to operate the clutch instead of spring force
• Consists of weights pivoted at a point, which fly off due to centrifugal force when the engine speed increases
• The bell crank levels press the plate, which ultimately presses the clutch plate on the flywheel against the spring
• No clutch pedal is required to operate the clutch

Belt Drives

• A belt is a looped strip of flexible material used to mechanically link two or more rotating shafts, offering smooth transmission of power between shafts at a considerable distance.
• Belt drives are used to efficiently transmit power or to track relative movement.
• There are two types of belt drives: open belt drives and crossed belt drives.

Open Belt Drives

• Used to rotate the driven pulley in the same direction as the driving pulley.
• Power transmission results in one side of the pulley being more tightened than the other side.
• In horizontal drives, the tightened side is always kept on the lower side of two pulleys.

Crossed Belt Drives

• Used to rotate the driven pulley in the opposite direction of the driving pulley.
• Higher wrap values enable more power transmission, but bending and wear of the belt are important concerns.

Advantages of Belt Drives

• Simple and economical
• Don't require parallel shafts
• Provided with overload and jam protection
• Noise and vibration are damped out, increasing machinery life
• Lubrication-free and require less maintenance cost
• Highly efficient (up to 98%, usually 95%)
• Economical when the distance between shafts is very large

Disadvantages of Belt Drives

• Angular velocity ratio is not necessarily constant or equal to the ratio of pulley diameters due to slipping and stretching
• Heat buildup occurs
• Speed is limited to usually 35 meters per second
• Power transmission is limited to 370 kilowatts
• Operating temperatures are usually restricted to -35 to 85°C
• Adjustment of center distance or use of an idler pulley is necessary for wearing and stretching compensation

Clutches

• A mechanical device that engages and disengages power transmission from the driving shaft to the driven shaft
• One shaft is connected to an engine or power unit, while the other shaft provides output power for the work

Types of Clutches

• Friction clutch
  • Single plate clutch
  • Multiplate clutch
    • Wet
    • Dry
• Cone clutch
  • External
  • Internal
• Centrifugal clutch
• Semi-centrifugal clutch
• Conical spring clutch or Diaphragm clutch
  • Tapered finger type
  • Crown spring type
• Positive clutch
  • Dog clutch
• Spline clutch
• Hydraulic clutch
• Electromagnetic clutch
• Vacuum clutch
• Overrunning clutch or freewheel unit

Single Clutch Plate

• One of the most commonly used types of clutches in light vehicles
• Consists of a clutch plate, friction plate, pressure plate, flywheel, bearings, clutch spring, and not-bolts arrangement
• The clutch plate is a thin metallic disc with friction surfaces on both sides
• Working:
  • When the clutch pedal is pressed, the springs get compressed, and the pressure plate moves backward
  • The clutch plate becomes free between the pressure plate and flywheel, disengaging the clutch
  • The flywheel continues to rotate as long as the engine is running, and the clutch shaft speed reduces slowly and then stops rotating

Multiplate Clutch

• Uses multiple clutches to make frictional contact with a flywheel of the engine
• Increases the capacity of the clutch to transmit torque
• Working principle is the same as the single-plate clutch
• Used in heavy commercial vehicles, racing cars, and motorcycles for transmitting high torque
• Can be dry or wet, with wet clutches commonly used in automatic transmissions

Cone Clutch

• Uses two conical surfaces to transmit torque by friction
• The engine shaft consists of a female cone and a male cone
• The male cone is mounted on the splined clutch shaft to slide on it
• Working:
  • When the clutch is engaged, the friction surfaces of the male cone are in contact with the female cone
  • When the clutch pedal is pressed, the male cone slides towards the spring force, and the clutch is disengaged

Centrifugal Clutch

• Uses centrifugal force to operate the clutch instead of spring force
• Consists of weights pivoted at a point, which fly off due to centrifugal force when the engine speed increases
• The bell crank levels press the plate, which ultimately presses the clutch plate on the flywheel against the spring
• No clutch pedal is required to operate the clutch

Belt Drives

• A belt is a looped strip of flexible material used to mechanically link two or more rotating shafts.
• Belt drives offer smooth transmission of power between shafts at a considerable distance.
• Types of belt drives:
  • Open belt drive: used to rotate the driven pulley in the same direction of driving pulley.
  • Crossed belt drive: used to rotate driven pulley in the opposite direction of driving pulley.

Advantages of Belt Drives

• Simple and economical.
• No need for parallel shafts.
• Provides overload and jam protection.
• Noise and vibration are damped out.
• Machinery life is increased due to shock-absorption of load fluctuations.
• Lubrication-free.
• Low maintenance cost.
• Highly efficient (up to 98%).
• Economical when the distance between shafts is very large.

Disadvantages of Belt Drives

• Angular velocity ratio is not necessarily constant or equal to the ratio of pulley diameters due to slipping and stretching.
• Heat buildup occurs.
• Speed is limited to usually 35 meters per second.
• Power transmission is limited to 370 kilowatts.
• Operating temperatures are usually restricted to -35 to 85°C.
• Some adjustment of center distance or use of an idler pulley is necessary for wearing and stretching of belt drive compensation.

Clutches

• A clutch is a mechanical device that specifically engages and disengages power transmission from the driving shaft to the driven shaft.
• Types of clutches:
  • Friction clutch
  • Single plate clutch
  • Multiplate clutch
  • Cone clutch
  • Centrifugal clutch
  • Semi-centrifugal clutch
  • Conical spring clutch or Diaphragm clutch
  • Positive clutch
  • Spline clutch
  • Hydraulic clutch
  • Electromagnetic clutch
  • Vacuum clutch
  • Overrunning clutch or freewheel unit

Single Plate Clutch

• Used in most modern light vehicles.
• Consists of a clutch plate, friction plate, pressure plate, flywheel, bearings, clutch spring, and not-bolts arrangement.
• The clutch plate is a thin metallic disc with both side friction surfaces.
• The pressure plate is bolted to the flywheel through a clutch spring, which provides the axial force to keep the clutch engaged.

Working of Single Plate Clutch

• When the clutch pedal is pressed, the pressure plate moves backward, and the clutch plate becomes free between the pressure plate and flywheel.
• This disengages the clutch and allows gear shifting.
• When the clutch pedal is released, the pressure plate returns to its original position, and the clutch is again engaged.

Multiplate Clutch

• Used in heavy commercial vehicles, racing cars, and motorcycles for transmitting high torque.
• Consists of multiple clutches to make frictional contact with a flywheel of the engine.
• The increased number of friction surfaces increases the capacity of the clutch to transmit torque.
• Can be either dry or wet.

Cone Clutch

• Uses two conical surfaces to transmit torque by friction.
• The engine shaft consists of a female cone and a male cone mounted on the splined clutch shaft.
• The advantage of using a cone clutch is that the normal force acting on the friction surface is greater than the axial force.

Centrifugal Clutch

• Uses centrifugal force to keep the clutch in the engaged position.
• No clutch pedal is required to operate the clutch.
• The clutch is operated automatically depending on the engine speed.
• Makes it easy for the driver to stop the vehicle in any gear without stalling the engine.

Gears and Gear Teeth

• Gears transmit motion by engaging teeth, which act as small levers, and are highly efficient (~95%) due to rolling contact between teeth.
• Gear teeth allow positive engagement, enabling high forces to be transmitted while minimizing friction.

Classification of Toothed Wheels

• Gears can be classified according to the relative position of the axes of revolution:
  • Connecting parallel shafts (e.g., spur gears, helical gears)
  • Connecting intersecting shafts (e.g., bevel gears)
  • Neither parallel nor intersecting shafts (e.g., helical gears, worm and worm gear)

Types of Gears

• Spur gears:
  • Most common type of gear
  • Teeth are perpendicular to the face of the gear
  • Limited to parallel shaft applications
  • Can be noisy and stressful on gear teeth
• Helical gears:
  • Teeth are cut at an angle to the face of the gear
  • Operate smoothly and quietly
  • Can be used for parallel or perpendicular shaft applications
  • Greater surface contact allows for higher loads
• Bevel gears:
  • Used to change direction of rotation
  • Teeth can be straight, spiral, or hypoid
  • Can be designed for various angles
• Worm and worm gear:
  • Used for large gear reductions (e.g., 20:1 or greater)
  • Worm can easily turn the gear, but not vice versa, due to friction
  • Common in conveyor systems and high-performance vehicles

Terms Used in Gears

• Addendum: Radial distance between pitch circle and top of teeth
• Dedendum: Radial distance between bottom of tooth and pitch circle
• Base Circle: Circle from which involute curve is generated
• Center Distance: Distance between centers of two gears
• Circular Pitch: Millimeters of pitch circle circumference per tooth
• Contact Ratio: Ratio of length of arc of action to circular pitch

Fundamental Law of Gear-Tooth Action

• A common normal to the tooth profiles at their point of contact must pass through a fixed point on the line of centers called the pitch point.
• Velocity ratio is equal to the inverse ratio of the diameters of pitch circles.

Conjugate Profiles

• Tooth profiles that satisfy the fundamental law of gear-tooth action
• Involute and cycloidal profiles are commonly used
• Involute profile is easy to manufacture and allows for varying center distance without changing velocity ratio

Generation of Involute Curve

• Involute curve is the path traced by a point on a line as it rolls without slipping on the circumference of a circle

• Can be defined as a path traced by the end of a string as it is unwrapped from a circle### Interference in Gears

• Interference between two teeth can be prevented if the point of contact is always on the involute profiles and if the addendum circles of the two mating gears cut the common tangent to the base circles at the points of tangency.

• To avoid interference, the following can be done:

  • Reduce the height of the teeth
  • Use undercut of the radial flank of the pinion
  • Increase the centre distance, which leads to an increase in pressure angle
  • Use a minimum number of teeth on the pinion (t) and wheel (T) to avoid interference

Backlash

• Backlash is the gap between the non-drive face of the pinion tooth and the adjacent wheel tooth
• Backlash is the error in motion that occurs when gears change direction
• The term "backlash" can also refer to the size of the gap

Practice Problem

• Given a module of 8 mm, a pressure angle of 20°, a larger gear with 57 teeth, and a pinion with 23 teeth, and an addendum of 1 module (8 mm)
• Pitch circle radius of the pinion (r) = mt = 92 mm
• Pitch circle radius of the gear (R) = mT = 228 mm
• Addendum circle radius of the pinion (ra) = r + addendum = 100 mm
• Addendum circle radius of the gear (RA) = R + addendum = 236 mm
• Length of path of contact (KL) = 39.76 mm
• Length of arc of contact = 42.31 mm
• Number of pairs of teeth in contact = (length of arc of contact) / (circular pitch)

Gears and Gear Teeth

• Gears transmit motion by engaging teeth, which act as small levers, and are highly efficient (~95%) due to rolling contact between teeth.
• Gear teeth allow positive engagement, enabling high forces to be transmitted while minimizing friction.

Classification of Toothed Wheels

• Gears can be classified according to the relative position of the axes of revolution:
  • Connecting parallel shafts (e.g., spur gears, helical gears)
  • Connecting intersecting shafts (e.g., bevel gears)
  • Neither parallel nor intersecting shafts (e.g., helical gears, worm and worm gear)

Types of Gears

• Spur gears:
  • Most common type of gear
  • Teeth are perpendicular to the face of the gear
  • Limited to parallel shaft applications
  • Can be noisy and stressful on gear teeth
• Helical gears:
  • Teeth are cut at an angle to the face of the gear
  • Operate smoothly and quietly
  • Can be used for parallel or perpendicular shaft applications
  • Greater surface contact allows for higher loads
• Bevel gears:
  • Used to change direction of rotation
  • Teeth can be straight, spiral, or hypoid
  • Can be designed for various angles
• Worm and worm gear:
  • Used for large gear reductions (e.g., 20:1 or greater)
  • Worm can easily turn the gear, but not vice versa, due to friction
  • Common in conveyor systems and high-performance vehicles

Terms Used in Gears

• Addendum: Radial distance between pitch circle and top of teeth
• Dedendum: Radial distance between bottom of tooth and pitch circle
• Base Circle: Circle from which involute curve is generated
• Center Distance: Distance between centers of two gears
• Circular Pitch: Millimeters of pitch circle circumference per tooth
• Contact Ratio: Ratio of length of arc of action to circular pitch

Fundamental Law of Gear-Tooth Action

• A common normal to the tooth profiles at their point of contact must pass through a fixed point on the line of centers called the pitch point.
• Velocity ratio is equal to the inverse ratio of the diameters of pitch circles.

Conjugate Profiles

• Tooth profiles that satisfy the fundamental law of gear-tooth action
• Involute and cycloidal profiles are commonly used
• Involute profile is easy to manufacture and allows for varying center distance without changing velocity ratio

Generation of Involute Curve

• Involute curve is the path traced by a point on a line as it rolls without slipping on the circumference of a circle

• Can be defined as a path traced by the end of a string as it is unwrapped from a circle### Interference in Gears

• Interference between two teeth can be prevented if the point of contact is always on the involute profiles and if the addendum circles of the two mating gears cut the common tangent to the base circles at the points of tangency.

• To avoid interference, the following can be done:

  • Reduce the height of the teeth
  • Use undercut of the radial flank of the pinion
  • Increase the centre distance, which leads to an increase in pressure angle
  • Use a minimum number of teeth on the pinion (t) and wheel (T) to avoid interference

Backlash

• Backlash is the gap between the non-drive face of the pinion tooth and the adjacent wheel tooth
• Backlash is the error in motion that occurs when gears change direction
• The term "backlash" can also refer to the size of the gap

Practice Problem

• Given a module of 8 mm, a pressure angle of 20°, a larger gear with 57 teeth, and a pinion with 23 teeth, and an addendum of 1 module (8 mm)
• Pitch circle radius of the pinion (r) = mt = 92 mm
• Pitch circle radius of the gear (R) = mT = 228 mm
• Addendum circle radius of the pinion (ra) = r + addendum = 100 mm
• Addendum circle radius of the gear (RA) = R + addendum = 236 mm
• Length of path of contact (KL) = 39.76 mm
• Length of arc of contact = 42.31 mm
• Number of pairs of teeth in contact = (length of arc of contact) / (circular pitch)

Gears and Gear Teeth

• Gears transmit motion by engaging teeth, which act as small levers, and are highly efficient (~95%) due to rolling contact between teeth.
• Gear teeth allow positive engagement, enabling high forces to be transmitted while minimizing friction.

Classification of Toothed Wheels

• Gears can be classified according to the relative position of the axes of revolution:
  • Connecting parallel shafts (e.g., spur gears, helical gears)
  • Connecting intersecting shafts (e.g., bevel gears)
  • Neither parallel nor intersecting shafts (e.g., helical gears, worm and worm gear)

Types of Gears

• Spur gears:
  • Most common type of gear
  • Teeth are perpendicular to the face of the gear
  • Limited to parallel shaft applications
  • Can be noisy and stressful on gear teeth
• Helical gears:
  • Teeth are cut at an angle to the face of the gear
  • Operate smoothly and quietly
  • Can be used for parallel or perpendicular shaft applications
  • Greater surface contact allows for higher loads
• Bevel gears:
  • Used to change direction of rotation
  • Teeth can be straight, spiral, or hypoid
  • Can be designed for various angles
• Worm and worm gear:
  • Used for large gear reductions (e.g., 20:1 or greater)
  • Worm can easily turn the gear, but not vice versa, due to friction
  • Common in conveyor systems and high-performance vehicles

Terms Used in Gears

• Addendum: Radial distance between pitch circle and top of teeth
• Dedendum: Radial distance between bottom of tooth and pitch circle
• Base Circle: Circle from which involute curve is generated
• Center Distance: Distance between centers of two gears
• Circular Pitch: Millimeters of pitch circle circumference per tooth
• Contact Ratio: Ratio of length of arc of action to circular pitch

Fundamental Law of Gear-Tooth Action

• A common normal to the tooth profiles at their point of contact must pass through a fixed point on the line of centers called the pitch point.
• Velocity ratio is equal to the inverse ratio of the diameters of pitch circles.

Conjugate Profiles

• Tooth profiles that satisfy the fundamental law of gear-tooth action
• Involute and cycloidal profiles are commonly used
• Involute profile is easy to manufacture and allows for varying center distance without changing velocity ratio

Generation of Involute Curve

• Involute curve is the path traced by a point on a line as it rolls without slipping on the circumference of a circle

• Can be defined as a path traced by the end of a string as it is unwrapped from a circle### Interference in Gears

• Interference between two teeth can be prevented if the point of contact is always on the involute profiles and if the addendum circles of the two mating gears cut the common tangent to the base circles at the points of tangency.

• To avoid interference, the following can be done:

  • Reduce the height of the teeth
  • Use undercut of the radial flank of the pinion
  • Increase the centre distance, which leads to an increase in pressure angle
  • Use a minimum number of teeth on the pinion (t) and wheel (T) to avoid interference

Backlash

• Backlash is the gap between the non-drive face of the pinion tooth and the adjacent wheel tooth
• Backlash is the error in motion that occurs when gears change direction
• The term "backlash" can also refer to the size of the gap

Practice Problem

• Given a module of 8 mm, a pressure angle of 20°, a larger gear with 57 teeth, and a pinion with 23 teeth, and an addendum of 1 module (8 mm)
• Pitch circle radius of the pinion (r) = mt = 92 mm
• Pitch circle radius of the gear (R) = mT = 228 mm
• Addendum circle radius of the pinion (ra) = r + addendum = 100 mm
• Addendum circle radius of the gear (RA) = R + addendum = 236 mm
• Length of path of contact (KL) = 39.76 mm
• Length of arc of contact = 42.31 mm
• Number of pairs of teeth in contact = (length of arc of contact) / (circular pitch)

Gears and Gear Teeth

• Gears transmit motion by engaging teeth, which act as small levers, and are highly efficient (~95%) due to rolling contact between teeth.
• Gear teeth allow positive engagement, enabling high forces to be transmitted while minimizing friction.

Classification of Toothed Wheels

• Gears can be classified according to the relative position of the axes of revolution:
  • Connecting parallel shafts (e.g., spur gears, helical gears)
  • Connecting intersecting shafts (e.g., bevel gears)
  • Neither parallel nor intersecting shafts (e.g., helical gears, worm and worm gear)

Types of Gears

• Spur gears:
  • Most common type of gear
  • Teeth are perpendicular to the face of the gear
  • Limited to parallel shaft applications
  • Can be noisy and stressful on gear teeth
• Helical gears:
  • Teeth are cut at an angle to the face of the gear
  • Operate smoothly and quietly
  • Can be used for parallel or perpendicular shaft applications
  • Greater surface contact allows for higher loads
• Bevel gears:
  • Used to change direction of rotation
  • Teeth can be straight, spiral, or hypoid
  • Can be designed for various angles
• Worm and worm gear:
  • Used for large gear reductions (e.g., 20:1 or greater)
  • Worm can easily turn the gear, but not vice versa, due to friction
  • Common in conveyor systems and high-performance vehicles

Terms Used in Gears

• Addendum: Radial distance between pitch circle and top of teeth
• Dedendum: Radial distance between bottom of tooth and pitch circle
• Base Circle: Circle from which involute curve is generated
• Center Distance: Distance between centers of two gears
• Circular Pitch: Millimeters of pitch circle circumference per tooth
• Contact Ratio: Ratio of length of arc of action to circular pitch

Fundamental Law of Gear-Tooth Action