Hooks Coupling Lab Report (Mechanical)

Introduction

A universal joint or flexible coupling is basically consisted of two shafts for transmitting circular
motion from one link to other link. A universal joint or a flexible coupling is a joint which transmits
rotational motion from one axis to another axis easily. Main advantage of universal joint is it can work with large angles between the shafts or between two axes. Normally minimum lower limit angle is 30. In normal use if the angle between two links is minor than 30 degrees a flexible coupling is used. Universal joints are used when the angles between links are international. There are two types of universal joints
• Hooke’s or Cardan Coupling
• Constant Velocity Joint
Even though these names are often used, the name individually does not give the specific differences
between hook’s and constant couplings. Basically a Hooke’s coupling has a fixed arm and the constant
velocity joint has variable arm.

Objectives

 To identify the correlation of velocity and displacement variations of single joint in different
angles
 To prove that the variation in displacement is discarded when two joints are used together
with the same intermediate angle α.

Apparatus

Figure 1 Hook's Coupling(link below)


https://extraessay.top/?sub_id=3kbl113lk4dg9iiph79

1) Baseboard
2) Sector scale-left hand
3) Pivoting base
4) Scale Disc
5) Bracket
6) Double Hooke’s coupling
7) Clamp Screw
8) Circular Scale
9) Cursor Block
10) Product Label
11) Pivot Shaft
12) Sector Scale-Right

Theory

Θ= Load (Input or drive shaft angle) 

ϕ = Output or driven shaft angle

α = the angle between two axles with respect to each other, when angle is zero the two shafts are parallel

Case I – Shafts are parallel, α = 0

Figure 1 – Hook’s Joint rotation planes α = 0 (Drawn in AutoCAD)

     

X1 = (      )                                       Y1 = ( )

Figure 2 – Hook’s Joint rotation planes α 0 (Drawn in AutoCAD)

Methodology

·         Hooke’s Coupling experiment was conducted in two stages as experiment 1 and experiment 2.

·         In experiment 1, firstly the angle between the shafts (α₁) was set to 45^⁰ and other joint was set to be straight (α₂=0^⁰)

·         Next the input scale disc was initialized to zero and the reading of the output shaft was noted by observing the scale.

·         Afterwards, input shaft was rotated by 10^⁰ up to 360^⁰ and all corresponded output values were noted on each rotation.

·         Experiment 1 was concluded after taking all output values for each input angles.

·         In experiment 2, both α₁ and α₂ were set to 30^⁰ and above procedure was again repeated to take output values for corresponded angles.

·         Experiment 2 was concluded after taking all output values and results of experiment 1 and experiment 2 were taken for further calculations and analysis.

Results

Observations of angles

Input (θ⁰)	Output (φ⁰)α=45	Output (φ⁰)α=30	tanθ	tanφ α2=0	Tanφ α1 = α2 = 30	Angular velocity(α2=0)	Angular velocity(α1 = α2 = 30)
0	6	4	0	0.1051	0.0699	1.414	2
10	18	10	0.1763	0.3249	0.1763	1.372611	1.8341
20	29	21	0.364	0.5543	0.3839	1.265916	1.4805
30	41	31	0.5774	0.8693	0.6009	1.1312	1.1429
40	51	40	0.8391	1.2349	0.8391	1.000583	0.8930
50	60	52	1.1918	1.7321	1.2799	0.891088	0.7245
60	69	61	1.7321	2.6051	1.804	0.808	0.6154
70	77	72	2.7475	4.3315	3.0777	0.750921	0.5481
80	84	83	5.6713	9.5144	8.1443	0.717822	0.5116
90	92	94	1.63E+16	-28.6363	-14.3007	0.707	0.5000
100	100	103	-5.6713	-5.6713	-4.3315	0.717822	0.5116
110	107	114	-2.7475	-3.2709	-2.246	0.750921	0.5481
120	115	124	-1.7321	-2.1445	-1.4826	0.808	0.6154
130	124	134	-1.1918	-1.4826	-1.0355	0.891088	0.7245
140	134	143	-0.8391	-1.0355	-0.7536	1.000583	0.8930
150	144	154	-0.5774	-0.7265	-0.4877	1.1312	1.1429
160	157	163	-0.364	-0.4245	-0.3057	1.265916	1.4805
170	172	172	-0.1763	-0.1405	-0.1405	1.372611	1.8341
180	186	183	0	0.1051	0.0524	1.414	2.0000
190	197	195	0.1763	0.3057	0.2679	1.372611	1.8341
200	210	202	0.364	0.5774	0.404	1.265916	1.4805
210	222	213	0.5774	0.9004	0.6494	1.1312	1.1429
220	231	222	0.8391	1.2349	0.9004	1.000583	0.8930
230	240	233	1.1918	1.7321	1.327	0.891088	0.7245
240	249	243	1.7321	2.6051	1.9626	0.808	0.6154
250	256	253	2.7475	4.0108	3.2709	0.750921	0.5481
260	265	264	5.6713	11.4301	9.5144	0.717822	0.5116
270	273	274	5.44E+15	-19.0811	-14.3007	0.707	0.5000

280	280	285	-5.6713	-5.6713	-3.7321	0.717822	0.5116
290	287	294	-2.7475	-3.2709	-2.246	0.750921	0.5481
300	295	303	-1.7321	-2.1445	-1.5399	0.808	0.6154
310	304	313	-1.1918	-1.4826	-1.0724	0.891088	0.7245
320	315	322	-0.8391	-1	-0.7813	1.000583	0.8930
330	324	331	-0.5774	-0.7265	-0.5543	1.1312	1.1429
340	339	341	-0.364	-0.3839	-0.3443	1.265916	1.4805
350	350	350	-0.1763	-0.1763	-0.1763	1.372611	1.8341
360	365	361	0	0.0875	0.0175	1.414	2.0000

(I did not include the & graphing analysis part. Please kind enough to do it by your own.)

Discussion

v  According to the above gain values for the angular velocities of the output shafts we can clearly noticed that when the shaft angles increasing, the angular velocities get raised.

v  According to graphs plotted using the experiment 1 and 2 we can clearly notice that they are showing graph and the tanθ increases the tanϕ also increase. Gradients of the two

graphs are equal to           .

    

v  Advantages of Hook’s Coupler

•        Simple in Construction

•        Hook’s Coupler can connect intersection and two non-parallel axes shafts

•        Large range of angular displacement

•        Able to take high toques

•        High toque transmission efficiency

v  Disadvantages of Hook’s Coupler

•        Cannot be used for high speed applications.

•        If driving shaft rotating with constant speed and driven shaft is rotating with acceleration.

•        Lubrications are required to reduce wear

•        Generates inertia torque on the driven shaft.

•        Often maintenances are required

•        Doesn’t support axial misalignment

•        Fluctuating motion of the joint

v  Applications

•                      Transmit power from gear box to rear axle in automobile vehicles.

In automobiles engine generates the power, but the power must be transmitted to the wheels to move the vehicle. The power generates from the engine goes through the clutch plate and the gear box to the rear axle by tubular propeller shaft. Propeller shaft consist of hook’s joints. These joints allow the propeller shaft to move liner when the wheels of the vehicle are running in the uneven surfaces.

•                      Transmit the drives to different spindles of multi-spindle drilling machine.

Multiple-spindle drilling machines are used to mass productions, and it is a great time saver and it increases the productivity of the machine system. It can drill multiple holes in multiple work pieces at the same time with high accuracy. As name it suggest it has multiple spindles driven by single power head. Spindles are constructed to change the distance from the center. Drill head can adjust any position depending work requirement. To adjust the center distance the spindles are connected to the main drive by hook’s joint (universal joint).

Conclusion

As the conclusion, using the Hooke’s Coupling Apparatus, displacement variation of a single joint at different angles has been observed. By the experiment, it shows that fixed link coupling is used for the circular motion transmission from one link to another. The experiment shows the behavior of the displacement and periodic speed also can be observed by changing the two shaft angles, such change or the fluctuation normally cannot bear in real world machinery. Hence it is very common to have intermediate e shaft with two couplings. Fluctuations will be introduced by the second coupling in opposite and equal direction, hence the overall output will be  a smooth transmission  in real world  use. But both the output and input shaft should create the equal angles to the intermediate shaft. That can be negligible with a low percentage error. The experiment’s objective to prove that when two joints are combined together with the equal intermediate angle, hence displacement variation is cancelled out.

 Reference

·         How a Car Works [Online]

Available at -: https://www.howacarworks.com/basics/how-the-transmission-works [Accessed on 19^th of April 2019]

·         Author Stream [Online]

Available at -: http://www.authorstream.com/Presentation/nilekar-1113953-hooke-s-joint/ [Accessed on 20^th of April 2019]

·         Design & development of multi spindle drilling head (msdh) [Online]

Available at -: http://www.iosrjournals.org/iosr-jmce/papers/sicete(mech)-volume1/11.pdf [Accessed on 17^th of April 2019]

·         Stock Drive Products -Sterling Instruments [Online]

Available at -: https://sdp-si.com/catalogs/D757-Couplings-Universal-Joints3.php [Accessed on 19^th of April 2019]