2. GUJARAT POWER ENGINEERING & RESEARCH INSTITUTE SUB : KINEMATICS OF MACHINES CODE : 2131906

3. Name Vikas Patel Ashvin Prajapati Bhaumik Prajapati Bunti Prajapati Pankaj Prajapati Pratik Patel Enroll. No. 131040119047 131040119049 131040119050 131040119051 131040119052 131040119053

4. GEAR…..  Power transmission is the movement of energy from its place of generation to a location where it is applied to performing useful work.  A gear is a component within a transmission device that transmits rotational force to another gear or device.

5.  Pitch surface : The surface of the imaginary rolling cylinder (cone, etc.) that the toothed gear may be considered to replace.  Pitch circle: A right section of the pitch surface.  Addendum circle: A circle bounding the ends of the teeth, in a right section of the gear.  Root (or dedendum) circle: The circle bounding the spaces between the teeth, in a right section of the gear. Terms used in Gears : Terminology

6.  Addendum : The radial distance between the pitch circle and the addendum circle.  Dedendum : The radial distance between the pitch circle and the root circle.  Clearance : The difference between the dedendum of one gear and the addendum of the mating gear.  Face of a tooth: That part of the tooth surface lying outside the pitch surface. Conti…

7.  Flank of a tooth: The part of the tooth surface lying inside the pitch surface.  Circular thickness (also called the tooth thickness) : The thickness of the tooth measured on the pitch circle. It is the length of an arc and not the length of a straight line.  Tooth space: The distance between adjacent teeth measured on the pitch circle.  Backlash: The difference between the circle thickness of one gear and the tooth space of the mating gear.  Backlash =Space width – Tooth thickness Conti…

8.  Circular pitch p: The width of a tooth and a space, measured on the pitch circle.  Diametral pitch P: The number of teeth of a gear per inch of its pitch diameter. A toothed gear must have an integral number of teeth.  The diametral pitch is, by definition, the number of teeth divided by the pitch diameter.  Module m: Pitch diameter divided by number of teeth.  The pitch diameter is usually specified in inches or millimeters; in the former case the module is the inverse of diametral pitch. Conti…

9.  Fillet : The small radius that connects the profile of a tooth to the root circle.  Pinion: The smaller of any pair of mating gears. The larger of the pair is called simply the gear.  Velocity ratio: The ratio of the number of revolutions of the driving (or input) gear to the number of revolutions of the driven (or output) gear, in a unit of time.  Pitch point: The point of tangency of the pitch circles of a pair of mating gears. Conti…

10.  Common tangent: The line tangent to the pitch circle at the pitch point.  Base circle : An imaginary circle used in involute gearing to generate the involutes that form the tooth profiles.  Arc of Contact: Locus of a point on the pitch circle from the beginning to the end of engagement of two mating gears is known as the arc of contact in fig. 3.22, APB or EPF is the arc of contact.  It has also been divided into sub-portions.  Arc of Approach: It is the portion of the arc of contact from the beginning of engagement to the pitch point, i.e. length AP or EP.  Arc of Recess: Portion of the arc of contact from the pitch point to the end of engagement is the arc of recess i.e. length PB or PF. Conti…

11.  Path of Contact or Contact Length: Locus of the point of contact between two mating teeth from the beginning of engagement to the end is known as the path of contact or the contact length.  Path of Approach : Portion of the path of contact from the beginning of engagement to the pitch point, i.e. the length CP.  Path of Recess : Portion of the path of contact from the pitch point to the end of engagement i.e. length PD. Conti…

12.  Line of Action or Pressure Line: The force, which the driving tooth exerts at point of contact of the two teeth.  This line is also the common tangent at the point of contact of the mating gears and is known as the line of action or the pressure line.  The component of the force perpendicular to the common tangent through the pitch point produces the required thrust. Conti…

13.  Pressure Angle or Angle of Obliquity (φ): The angle between pressure line and the common tangent to the pitch circles is known as the pressure angle or the angle of obliquity.  For more power ‘transmission and lesser pressure on the bearing pressure angle must be kept small. Standard pressure angles arc and 25°. Gears with 14.5° pressure angles have become almost obsolete. Conti…

14. Law of Gearing  The fundamental law of gearing states that the angular velocity ratio between the gears of a gear set must remain constant throughout the mesh.  The fig. shows the gear wheels rotation direction :  Also from similar triangels and

15. Conti…  The common normal to the two surfaces at the point of contact Q intersects the line of centres at point P.  In order to have a constant angular velocity ratio for all positions of the wheels, the point P must be the fixed point.  Law of gearing:  The common normal at the point of contact between a pair of teeth must always pass through the pitch point.

16. Involute and Cycloidal profile  An involute of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping.  Involute

17. Construction of involute  Let A be the string point of the involute. The base cricle is divided into no. of parts e.g. AP 1, P 1 P 2, P 2 P 3 etc.  The tangents at P 1, P 2, P 3 etc. are draw and the length P 1 A 1, P 2 A 2, P 3 A 3 equal to the arcs AP 1, AP 2 and AP 3 are set off.  Joining the points A, A 1, A 2, A 3 etc. we obtain the involute curve AR.  A little consideration will show that at any instant A 3, the tangent A 3 T to the involute is perpendicular to P 3 A 3 and P 3 A 3 is the normal to the involute.  In other words, normal at any point of an involute to the circle.

18. 17 Conti…

19.  A cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line.  When a circle rolls without slipping on the outside of a fixed circle, the curved traced by a point on the circumference of a circle is known as epy-cycloid.  Cycloidal  When a circle rolls without slipping on the inside of a fixed circle, the curved traced by a point on the circumference of a circle is known as hypo-cycloid.

20. Comparision between involute and cycloidal gears Involute gears 1. The center distance for a pair of involute gears can be varried within limits without changing the velocity ratio. 2. The pressure angle from the start of the engagement of to the end of the engagement, remains constant. Cycloidal gears 1. This not true for cycloidal gears. Chfhdfhdhdfc dffhghghghdfdfg. 2. The pressure angle is maximum at the beginning of engagement of teeth, reduce to zero at pitch point, starts decreasing and again becomes maximum at the end of engagement. 19

21. Interference 20  Fig. shows a pinion with center O1, in mesh with wheel or gear with centre O2.  NM is the common tangent to the base circles and KL is the path of contact between the tow mating teeth.  A little consideration will show, that if radius of the addendum circle of pinion is increased to O1N, the point of contact L will from L to N.  When the radius is further increased, the point of contact L will be on the inside of base circle of wheel and not on the involute profile of tooth on wheel.  The tip of tooth on the pinion will then undercut the tooth on the wheelat the root and remove part of the involute profile of tooth on the wheel.  The phenomenon when the tip of tooth undercuts the root on its mating gear is known as interference.

22. Conti…  Interference may only be prevented, if the addendum circles of the two mating gears cut the common tangent to the base circles between the points of tangency.

23. Undercutting 22  Tip of the wheel will dig out or interfere with the flank of the pinion and remove the part of the material called undercut.  Process of removal of material is called undercutting. Base circle

24. Minimum number of teeth to avoid interference 23  Let, No of teeth on the pinion = t No of teeth on the wheel = T Pitch circle radius = r = m.t/2 G = gear ratio = T/t = R/r Addendum circle radius= r+1 module Dedendum circle radius = r- 1.157m Base circle radius =rcos φ

25. Minimum Number of Teeth on the Pinion and the wheel in Order to Avoid Interference 24 For Pinion, For Gear, Ap =addendum coefficient of pinion, addendum of pinion = Ap*m Aw =addendum coefficient of wheel, addendum of wheel = Aw*m

26. Contact Ratio (Number of Pairs of Teeth in Contact) 25  It is the Ratio of the length of the arc of contact to the circular pitch.

27. TYPES OF GEARS i. Spur gear ii. Helical gear iii. Rack and pinion iv. Bevel gear v. Worm and worm gears

28. SPUR GEAR  Teeth is parallel to axis of rotation.  Transmit power from one shaft to another parallel shaft.  Used in Electric screwdriver, oscillating sprinkler, windup alarm clock, washing machine and clothes dryer.

29. External and Internal spur Gear…

30. Helical Gear  The teeth on helical gears are cut at an angle to the face of the gear.  This gradual engagement makes helical gears operate much more smoothly and quietly than spur gears.  One interesting thing about helical gears is that if the angles of the gear teeth are correct, they can be mounted on perpendicular shafts, adjusting the rotation angle by 90 degrees.

31. Rack and pinion  Rack and pinion gears are used to convert rotation (From the pinion) into linear motion (of the rack)  A perfect example of this is the steering system on many cars

32. Bevel gears  Bevel gears are useful when the direction of a shaft's rotation needs to be changed.  They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well.  The teeth on bevel gears can be straight, spiral or hypoid.  locomotives, marine applications, automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection machines, etc.

33. Straight and Spiral Bevel Gears

34. WORM AND WORM GEAR  Worm gears are used when large gear reductions are needed. It is common for worm gears to have reductions of 20:1, and even up to 300:1 or greater.  Many worm gears have an interesting property that no other gear set has: the worm can easily turn the gear, but the gear cannot turn the worm.  Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc.