The pitch circle diameter of the smaller of the two spur wheels which mesh externally and have involute teeth is 100 mm. The number of teeth are 16 and 32. The pressure angle is 20° and the addendum is 0.32 of the circular pitch. Find the length of the path of contact of the pair of teeth.

The pitch circle diameter of the smaller of the two spur wheels which mesh externally and have involute teeth is 100 mm. The number of teeth are 16 and 32. The pressure angle is 20° and the addendum is 0.32 of the circular pitch. Find the length of the path of contact of the pair of teeth.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.73P

See similar textbooks

Related questions

Q: In the gear system shown, the motor applies a 190 lb-ft torque to the gear at A. A torque of Tc=392…

Q: A rotating shaft carries three unbalanced masses of 4 kg, 3 kg, and 2.4 kg at radial distances of 75…

Q: Shown below is a figure of a landing gear configuration on the VS and VD planes (for landing gear…

A: The given figure shows the landing gear configuration on the VS and VD planes (for landing gear the…

Q: A pair of spur gears with 20° tooth form transmits 1.0-hp. The pinion is mounted on the shaft of an…

Q: The aluminum alloy [G = 4000 ksi] pipe is fixed to the wall support at C. The bolt holes in the…

A: Shear modulus or Modulus of rigidity is the ratio of shear stress to shear strain. Torque is the…

Q: Two equal involute gear wheels of 40 teeth each, 3 mm module and 20° pressures angle are in mesh.…

A: According to the given data Number of teeth (T)=40 Module (m)=3mm Pressure angle ϕ=20° Speed…

Q: The circular shaft AB consists of a 19.5 mm diameter solid steel cylinder in which a 5.3 mm diameter…

Q: Perform "Design for stress" based on Machine Component Design knowledge

A: An introduction for the solution is:The answer begins with mechanical design principles, which are…

Q: Perform free body diagram analysis to get reaction force at bearings

A: Consider the shaft lies in xy - plane as shown below and draw free body diagram.Here indicates…

Q: A motor car has a wheel base of 2.82 m has pivot centres 1.8 m. The track distance between tyre…

Q: The figure shows an internal rim-type brake having an inside rim diameter of 11 in and a dimension R…

A: Brake is a mechanical device which absorbs energy from the moving system or any mechanism with the…

Q: The shaft is fixed at ends A and B and has a positive torque T a distance of 4m from A and 8m from…

Q: Find the value of the input torque on the crank-shaft mechanism in followin Figure. The centers of…

A: To carry out dynamic force analysis of the four-bar mechanism shown in the figure, it is required to…

Q: -2x Criven the shape above, Find the location of the Controid. Show all work.

A: Here, four shapes are visible so, No Shape Ai Xi Yi AiXi AiYi 1 Semi circle 5654.87 60 0…

Q: 8'-0" 91 006 900 lb 10'-0" B 400 Ib 68' – 0"| 48'-0" 12'-0" |

Q: A and d The teeth are of

Concept explainers

Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

100%

The pitch circle diameter of the smaller of the two spur wheels which mesh externally and have
involute teeth is 100 mm. The number of teeth are 16 and 32. The pressure angle is 20° and the
addendum is 0.32 of the circular pitch. Find the length of the path of contact of the pair of teeth.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

1.The pitch circle diameter of the smaller of the two spur wheels which mesh externally and have involute teeth is 100mm.The number of teeth are 16 and 32.The pressure angle is 20° and the addendum is 0.32 of the circular pitch.Find the length of the path of contact of the pair of teeth
5. The pitch circle diameter of the smaller of the two spur wheels which mesh externally and have involute teeth is 100 mm. The number of teeth are 16 and 32. The pressure angle is 20° and the addendum is 0.32 of the circular pitch. Find the length of the path of contact of the pair of teeth.
The number of teeth on the driving sprocket chain is 50, used to change up of speed from 500 r.p.m. to 850 r.p.m. Find the number of teeth on the driven sprocket. If the pitch circle diameter of the driven sprocket is 350 mm and center to center distance between the two sprockets is 1000 mm, determine the pitch and length of the chain.
In the image on the right, there is a red gear G1 on the left with a radius of r1 = 2.81cm. Gear G1 is locked to the green gear G2 with a radius of r2 = 0.734cm. Gear G2 then shares the same axle as the blue circular saw G3, which has a radius of r3 known to make a full rotation every T = 0.836s. Using at least 6 significant digits in your calculations, compute the following: V3! 12.8cm. Gear G1 is W1 a) The angular speed wi of gear G1. Remember that angular speed is measured in radians per T3 r2 unit time. G2 b) The rim speed vi of gear G1. Since gears G1 and G2 are locked together, the rim speed of G2 is also v1. G1 G3 c) The angular speed w2 of gear G2. Since gear G2 and saw G3 share the same axle, the angular speed of G3 is also w2. d) The rim speed v3 of saw G3.
Q1: The arrangement of a transmission brake is shown in the figure. The arms are pivoted at O and, when force is applied at the end of the hand lever, the screw AB will rotate. The left-and right- hand threads working in nuts on the ends of the arms will move the arms together and thus apply the brake actuating force equally. A B 12cm The drum is 17.75cm diameter, and the angle subtended by each block is 90°. the friction material lining width is 4cm. Assuming a coefficient of friction for the braking surfaces that is equal to 0.30 Determine the force required by the screw AB to set the brake torque on the drum equal to 200 N-m. 17 75cm 12cm 46 35cm Torqueleft= TorqueRight= 97.40 N.m 6 35cm 102.60 N.m
This shoulder bolt is composed of hot-rolled monel. The head of the shoulder bolt is a regular hexagon and it measures 6 mm across opposite flats. The other dimensions of the bolt are given below, as well as the forces to which this component is subjected. Find the change in length of each segment of the part as well as the overall change in length from A to D F_A = 4.8 kN F_B = 5.1 kN F_C =1.6 kN F_D = 1.9 kN a = 4mm b = 4.1 cm c = 6.8 cm d_s = 5 mm d_t (effective) = 3mm Assume:∙ Bearing stress between threads of the bolt and the nut may be neglected∙ Stress concentration effects may be neglected∙ The force that the nut applies may be treated as a concentrated force.∙ The nut may be treated as rigid.∙ The forces applied to the nut and the shoulders of the bolt are distributed evenly around their perimeters δAB = δBC = δCD = δoverall =
Two gears are designed to mesh as shown. Gear 1 is driven by another gear that is not shown which induces a force, F, equal to 52 N as shown. Gear 1 has 78 teeth and a pitch diameter equal to 64 mm. If Gear 2 has 44 teeth, and the gears are to remain at constant speed while the tangent force F is applied, find the Value of the resisting torque that is applied to Gear 2.  Direction that the resisting torque should be applied. Explain youranswer. Note: Gears are not drawn to scale.
Spur gear train is used to transmit the power of 2kW from input gear A rotating at 120 rpm to output gear D through a compound gear BC. The number of teeth on the gear A, B, C and D are 16, 32, 12 and 18 respectively. Given: Module = 4mm, pressure angle=20° The tangential force acting on the gear B is N A D В
Two parallel shafts have an angular velocity ratio of 4 to 1 are connected by gears, the largest of which has 40 teeth. Find the number of teeth of smaller gear.
Draw free-body diagrams of the two gears, assuming an input couple M on theOUT X shaft of the larger gear in the direction shown. Include forces at bearings A, B, D and E. M isthe reaction couple at the output shaft - i.e. the resistance to turning of the object being driven.The gears have 48 and 24 teeth respectively. If the input gear (large gear) turns at 100 rpm(= revolutions per minute), the output speed (small gear) is _______rpm.Wil OUT X IN Xl M be larger or smaller than M ?
In the gear system shown, the motor applies a 190 lb-ft torque to the gear at A. A torque of Tc = 392 lb-ft is removed from the shaft at gear C, and the remaining torque is removed at gear D. Assume that DA-4-in.-diameter, Dg=12-in.-diameter, L₁=56 in., and L₂-30 in. Segments (1) and (2) are solid 1.5-in.-diameter steel [G = 12200 ksi] shafts, and the bearings shown allow free rotation of the shaft. Determine: (a) the maximum shear stresses T₁, T₂ in segments (1) and (2) of the shaft. (b) the rotation angle D/B of gear D relative to gear B. Answers: (a) T₁ (b) D/B = = i ᎠᏴ ; A DA i B L₁ Tc amala ksi, T₂ = L2 i Tp D ksi.
The electric motor exerts a 500-N-m torque on the aluminum shaft ABCD when it is rotating at a constant speed. The torques exerted on pulleys Band Care as shown. Take a = 1.4 m, b= 0.9 m, and G= 27 GPa. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 300 N. m 200 N. m 45 mm 44 mm 40 mm Im Determine the angle of twist between Band C. The angle of twist between Band Cis|