UNIVERSAL JOINT

Title; Universal Joint

Objective;

1. To ascertain how an energy can remove to different motion.
2. To calculate and analys how much motion can be transmitted by a universal joint.
3. To identify on which direction and angel the universal joint work in most efficience.

Theory;

The non-complicated way of transferring motion between non-coaxial shafts is by using one or two union sel joints. A common used in machinery and its function I to transfer rotation between the shaft that are not at parallel position to one and another.

In general, the angular motion is not uniformly transferred from the driving shaft to the driver shaft. The relationship between the angles of the driving shaft, O₁ and the driven shaft O₂ is;

cos y = tan O₁ tan O₂

where y is the angular misalignment of the shaft. This relationship can be derived

α₁ = α₂ =α₃ = 900. α₁ = y and Ø₁ = O₁ , Ø₂ = O₂ where α₁ and Ø₁ ( i = 1,2,3,4) are consistent. Substituting these values;

sin O₁ sin O₂ = cos O₁ cos O₂ = cos y = 0

the angular velocity relationship can be obtained by differentiating with respect to time gives;

tan O₂ = cos y cot O₁

Differentiating with respect with time gives;

O₂ sec² O₂ = O₁ sec² O₁ cos y

Hence the ratio of the magnitude of the haft velocities is;

O₂ = cos² O₂ cos y

O₁ sin² O₁

When the angular relationship between the axes of the drives elements is variable, the elements maybe joined by a flexible coupling, shaft or universal joint.

i. The Hooke type Universal Joint, the misalignment is indicated by the angle Ø. Velocity ratio w2 / w1 I instantaneously as the joint rotates.

ii. The cross-link of the universal joint is shown as it rotates through 90⁰.

When two universal joints are used, input / output speeds are equally distributed between both universal joints if each universal joint takes half of the misalignment as shown.

Procedure;

1. The rotational angle needle of both shaft are set to zero. The shaft angle of both shaft also set to zero.

2. The input shaft angle is set to 10º (Ψ) to make them misalignment and slowly rotate the input shaft to 30º (β). The rotational angle of output shaft (θ) is read and data is recorded.

3. The rotational angle of input shaft is added with other 30º until it reached 360º. Every addition of rotational angle of input shaft, take the reading of the rotational angle of output shaft.

4. Step 2 and 3 are repeated for changing the angle of input shaft angle to 20º, 30º, 45º, and 90

Apparatus;

Universal Joint

Readings;

Shaft angle (Ψ)	Rotational angle			Shaft angle (Ψ)	Rotational angle
	Input shaft(β)	Output shaft(θ)			Input shaft(β)	Output shaft(θ)
0º	0	2		15º	0	2
	30	33			30	32
	60	62			60	62
	90	91			90	92
	120	121			120	121
	150	151			150	150
	180	182			180	182
	210	212			210	213
	240	244			240	244
	270	268			270	273
	300	302			300	301
	330	332			330	337
	360	362			360	362

Shaft angle (Ψ)	Rotational angle			Shaft angle (Ψ)	Rotational angle
	Input shaft(β)	Output shaft(θ)			Input shaft(β)	Output Shaft(θ)
30º	0	2		45º	0	2
	30	31			30	36
	60	60			60	64
	90	87			90	86
	120	115			120	110
	150	145			150	139
	180	179			180	179
	210	212			210	217
	240	241			240	244
	270	267			270	266
	300	295			300	290
	330	326			330	320
	360	360			360	360

Result;

Table ratio of angular velocity of the input and output shaft

Shaft angle (Ψ)	Input shaft (β)	Ratio ωА ωВ		Shaft angle (Ψ)	Input shaft (β)	Ratio ωА ωВ
0º	0	1.000		15º	0	1.000
	30	0.967			30	1.000
	60	0.983			60	1.000
	90	1.000			90	1.011
	120	1.000			120	0.992
	150	0.993			150	0.993
	180	1.006			180	1.006
	210	1.005			210	1.010
	240	1.004			240	1.008
	270	1.004			270	1.004
	300	1.003			300	1.003
	330	1.003			330	1.003
	360	0.997			360	0.997

Shaft angle (Ψ)	Input shaft (β)	Ratio ωА ωВ		Shaft angle (Ψ)	Input shaft (β)	Ratio ωА ωВ
30º	0	1.000		45º	0	1.000
	30	1.100			30	1.333
	60	1.050			60	1.117
	90	1.000			90	1.000
	120	0.975			120	0.942
	150	0.987			150	0.947
	180	1.011			180	1.011
	210	1.029			210	1.047
	240	1.017			240	1.008
	270	1.004			270	0.996
	300	0.993			300	0.977
	330	0.994			330	0.979
	360	0.994			360	0.989

Graphs:

Below is the graph output shaft (θ) versus input (β) for:

Input shaft angle (Ψ) at 0°,

Below is the graph output shaft (θ) versus input (β) for:

Input shaft angle (Ψ) at 15°,

Below is the graph output shaft (θ) versus input (β) for:

Input shaft (Ψ) at 30°,

Below is the graph output shaft (θ) versus input (β) for:

Input shaft (Ψ) at 45°,

Calculation:

Given that

gradient = dβ

dθ

which equals to

x₂ – x₁

y₂ – y₁

From graph of Shaft B at the angle of 0°

Input shaft (β)	Output shaft (θ)	Gradient
0	0	0.0000
30	29	1.0345
60	59	1.0000
90	89	1.0000
120	119	1.0000
150	149	1.0000
180	179	1.0000
210	211	0.9375
240	241	1.0000
270	271	1.0000
300	301	1.0000
330	331	1.0000
360	360	1.0345

From graph of Shaft B at the angle of 15°

Input shaft (β)	Output shaft (θ)	Gradient
0	0	0.0000
30	29	0.9375
60	53	1.0345
90	88	1.1538
120	116	1.0714
150	147	1.0345
180	178	0.8571
210	209	0.9091
240	241	1.0000
270	269	1.1111
300	298	1.1538
330	329	1.0714
360	360	0.8108

From graph of Shaft B at the angle of 30°

Input shaft (β)	Output shaft (θ)	Gradient
0	0	0.0000
30	32	0.9375
60	61	1.0345
90	87	1.1538
120	115	1.0714
150	144	1.0345
180	179	0.8571
210	212	0.9091
240	242	1.0000
270	269	1.1111
300	295	1.1538
330	323	1.0714
360	360	0.8108

From graph of Shaft B at the angle of 45°

Input shaft (β)	Output shaft (θ)	Gradient
0	0	0.0000
30	38	0.7895
60	65	1.1111
90	85	1.5000
120	110	1.2000
150	146	0.8333
180	181	0.8571
210	219	0.7895
240	246	1.1111
270	268	1.3636
300	292	1.2500
330	322	1.0000
360	360	0.7895

Discussion;

The experiment shown the detail of value at angles angular speed and ratio of speed are tailored and related to each other which where by obtaining greater and higher value of angles will lead to a higher as well as greater value of angular speed and the same goes to the ratio of speed at the same time. Obtained are not the accurate; however the figure are correct and acceptable. The inaccurate of values obtained might be cause to the factor that the error of readings that were being taken during the experiment, such as, it can be best said as parallax error.

The used of universal joint are widely used in the engineering application. Some of the examples are as follows;

1. Automotive steering linkage.

For automotive steering linkage the important geometry is that the axes of the front should be concurrent at the axis of the rear wheel.

Since the axe of all four wheels meet at a common instanenous center, the wheel ca roll without cuffing action.

Universal joints are common wherever a driveshaft needs to turn a corner; a driveshaft with a universal joint can freely rotate through the universal joint, and no gears are required to couple the two ends. The most obvious example of this application of a universal joint is in the driveshafts of automobiles, a technology known as the Hotchkiss drive.

2. Industrial robot – computer controlled.

The arm works on the front, middle near of the body. As the body moves through the robot’s base line station. Abort and utility sequences are includes in the robot’ computer control.

Conclusion;

From the calculation of the experiment, the result we get was nearly the same with the theory. We interpret the universal joint when input rotation start, we found the velocity is same if shaft in position linear (0˚ both side). If position input change from 0˚ to 15˚, we find the value of velocity is different. From data, we take average data. We can simplify, the velocity is less than position linear. For the position angle is 30˚ and 45˚, the situation is same the angle 15˚. But the velocity for angle 30˚ and 45˚ is less than angle 15˚. When input have angle, it means the movement rotation slow than output movement. Friction will be occurring when joint at shaft. Actually the universal joint has 2 types. The 2 types is single and double universal joint. What we do in the lab is double universal joint

As a conclusion, we had successfully obtained the value of angular speed and rate of speed for both output shaft and input shaft.