Mechanical Analysis of a Gearless Elbow Transmission Mechanism
Adebayo Badmos and Fyzal Badarudeen
Mechanical Engineering
Higher Colleges of Technology
Al Ain Campus, UAE
Abstract
A three-pin gearless elbow transmission mechanism was designed and fabricated and the
operation was studied at different input torques and different angles between the input and out
shafts. The operation of the mechanism was simulated using the SolidWorks 3D software and
different pin materials were investigated for stress, strain, and deformation at varying input
torque and angles. Three input torques of 0.4, 0.8, and 1.5 Nm and six different angles from 0
to 90 degrees between the input and output shafts were investigated. Generally, and as should
be expected, the stress, strain, and deformation developed in the pin materials increase with the
input torque. The stress generally appears to decrease with the angle from 0 degrees to a
minimum at 30 degrees angle and then subsequently increases with the angle to its maximum
at 90 degrees. Whereas the strain also appears to decrease from 0 degrees to a minimum at 30
degrees, the value fluctuates with a pattern that appears repeated for two regions, 0-45 degrees
and 45 to 90 degrees with the values at 0 and 90 degrees the same. The deformation of the pin
materials shows a reverse pattern to that of the stress, increasing with the angle from 0 degrees
to its maximum at 30 degrees and then decreasing to its minimum at 90 degrees.
Keywords: Gearless elbow transmission, shafts angle, input torque, stress, strain, deformation
Introduction
The gearless elbow mechanism, also known as gearless transmission, or Orbital transmission
mechanism, is simple in construction and mainly used in place of bevel gears where the motion
is to be transmitted at 90⁰ [1]. The angle between the input and output shafts is generally taken
as 90⁰ [2, 4, 5, 6, 7, 8, 11, 12, 14, 15], however, the mechanism can also be used to transmit
power at varying angles [4, 10, 11, 14]. The mechanism is usually made with 3 L-pins but the
system operates more smoothly with increasing number of L-pins [9]. It system be used for any
shaft diameter [13] and whereas the efficiency of the gear drive is only up to 42%, the elbow
mechanism can go up to 90-92% efficiency [13].
Typically, odd numbers of pins are used and a minimum of 3 are required for the system to run.
The pins are inserted into holes on the cylindrical discs connected to the input and output shafts
and the motion is transmitted through the simultaneous sliding and rotating movement of the
pins. The mechanism studied in this work, shown in Figure 1, consists of 3 L-pins at an angular
spacing of 120⁰ and the power is supplied from a motor.
Figure 1: Layout of L-Pin Elbow Mechanism
Experimental Simulation and Analysis
The effect of input torque on the operation of the mechanism was studied with 3 input torques
of 0.4, 0.8, and 1.5 Nm, and the effect of angular orientation was investigated by varying the
angles between the input and output shafts from 0o to 90o, with 0o at the point where the two
shafts are aligned in a straight line. The experimental simulation was carried out with SolidWorks
3D modeling and simulation software. The operation of the mechanism was simulated to study
the stress, strain, and deformation developed in the pin material for each input torque at different
angles between the shafts. The effect of the pin material was also investigated using the
capability of the software to independently specify the materials for the individual model
components.
Results and Discussion
Stress versus Angular Orientation
Figure 2 shows the plot of stress for 1020-Steel as a function of the angle between the input and
output shafts for different input torques. The stress is shown to increase with torque as expected
with the maximum of the input torques investigated, 1.5 Nm, producing the highest stress, and
the minimum torque, 0.4 Nm, the least stress for all the angles studied. For each torque, the
stress is shown to fall continuously with an increasing angle to a minimum value at the same
angle of 30o, then rises but fluctuates between 30 and 60o then rises continuously with the
increasing angle from 60 to 90o.
1020 Steel-0.4 Nm Torque
30.000
120.000
100.000
26.000
Stress, MPa
Stress, MPa
28.000
24.000
22.000
80.000
60.000
40.000
20.000
20.000
0
a
0.4 Nm-Torque
0.8 Nm-Torque
1.5Nm-Torque
1020 STEEL
20
40
60
Angle
80
100
0.000
b
0
50
Angle
Figure 2: Stress versus orientation angle (a) and effect of input speed (b)
100
Strain versus Angular Orientation
Figure 3 shows the plot of strain as a function of the angle for different input torques. The pattern
is similar to that of the stress with the strain increases with increasing torque. For all the input
torques, the strain is also shown to decrease continuously with an increasing angle to a minimum
value at an angle of 30o for all the torques. Subsequently, the value increases generally with
increasing angles, however, it fluctuates alternately between angles from 30 to 90o.
1020 Steel: 0.4 Nm - Torque
0.4 Nm-Torque
0.8 Nm-Torque
1.5 Nm-Torque
1020 STEEL
75
300
70
250
65
200
60
Strain
Strain
80
55
50
100
45
50
40
0
a
150
20
40
60
80
100
Angle
0
b
0
Angle
50
100
Figure 3: Strain versus orientation angle (a) and effect of input speed (b)
Deformation versus Angular Orientation
Figure 4 shows the plot of deformation as a function of the angle for the different input torques.
The deformation is shown to increase with torque as observed for the stress and strain. For
each torque, the deformation increases continuously with an increasing angle to the maximum
value at the same angle of 30o, it then falls continuously with the increasing angle to 90o.
1020 Steel: 0.4 Nm -Torque
0.5
1.6
Deformation, mm
0.4
Deformation
0.4 Nm-Torque
0.8 Nm-Torque
1.5 Nm-Torque
1020 STEEL
0.3
0.2
0.1
1.2
0.8
0.4
0
0
a
50
100
0
Angle
b
0
50
Angle
100
Figure 4: Deformation versus orientation angle between shafts at different speeds
Conclusions
Experiments and simulations have been used to conduct a mechanical analysis of a 3-pin
gearless transmission mechanism to investigate the effect of the input torque and the angle
between the input and output shafts on the stress, strain, and deformation developed in the pin
material. The following observations were made:
1. The stress, strain and deformation developed the pin material increase with increasing
input torque
2. Stress decreases with increasing angle to a minimum at an angle of 30o for all the torques,
fluctuates from 30-60o then increases continuously to 90o.
3. Strain pattern is similar to that of the stress but fluctuates between alternate angles from
30-90o.
4. Deformation increases with increasing angle to the angle of 30o then decreases with
increasing angle to 90o.
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