MECHANICAL DESIGN
DESIGN PARAMETERS
Payload = Weight to be lifted = 100gms =0.1 kg
1) DESIGN OF END EFFECTOR
Force exerted due to gravity = 0.1x 9.8= 0.98 N
Assuming gripping material as rubber and a friction factor = m =0.25 we have
Normal force =f = f/m= 0.98/0.25 =3.92N
Torque required to exert this force on end of arm = f x L
= 3.92 x 0.085 = 0.272 N-m
Here we are using a worm gear pair with a reduction of 1:40
Hence the torque required to lift = 0.272/40 =0.0068 N-m
This is shared by two arms hence .0068/2=0.0034 N-m
This is equal to 0.034/9.81 x 100=0.0347 Kg-cm
The stepper motor used is a 0.3 Kg-cm motor which is commercially available. Thus giving a factor of safety (f.o.s.) of almost 10.
GRIPPER LINKAGE MECHANISM
In order to keep the gripper ends parallel to each other a 4-bar linkage
mechanism has been used as shown in the fig the distance between the parallel wires is constant at 13mm. As a result when the angular movement of the arm takes place during opening and closing of the gripper the gripper arm tip moves such that the ends remain parallel.
GEAR MECHANISM
For the end effector a worm gear mechanism has been used .it consists of a worm shaft and two worm wheels .the material used is Teflon. Since the material
Shear stress value is 58 N/mm2 and the maximum torque on the assembly is 3.92 N-m the design is safe.
THE WORM GEAR SPECIFICATION
Module 0.75
Worm shaft diameter=8mm
Worm shaft length=30mm
No of starts=1
Worm wheel diameter=33mm
No of teeth=42
Center distance between gears = 37mm
Material shear strength=58 N/mm2
END EFFECTOR SPECIFICATION
Motor used - 0.3 Kg-cm
Mechanical support - aluminium
Gears - Teflon worm gears
Tool holder - wood with rubber lining
Overall length = 176mm
Over all weight = 500gm
Max opening = 150mm
Gripper end dimension = 27 x 22 x 15
2) WRIST ROLL DESIGN
Shaft connected to the gripper unit has a diameter of 12 mm. the shaft has been connected to the gripper assembly by means of a plate connected to the motor with the help of screws.
DESIGN OF SLEEVE
The shaft which has a diameter of 12 mm is connected to the sleeve .The sleeve is a multi –purpose unit which apart from housing the sleeve, houses a gear and ends in a bearing in the bearing housing. The sleeve has a diameter of 25 mm with a hole of 12 mm into which the wrist shaft goes this is of length 25 mm. Next comes a step of O.D15 mm ,length 50 mm to accommodate a gear , and also houses the bearing in the bearing housing.
DESIGN OF SLEEVE SHAFT
The diameter of the shaft varies from 12mm to 25mm considering the least dia as the design criterion we have:
s = M /Z
= force x distance / p x d3 /32
= 0.9 kg x 9.81 x 250 x 32 /p x 123
= 13 N/mm3
The normal stress being 78 N/mm3
Hence we get a f.o.s. of almost 6.
SLEEVE SPECIFICATION
It is a stepped shaft of dimensions:
1.Material = mild steel
1.O.D 25 mm length 30mm
2.O.D 15 mm length 50 mm
3. Approx. weight = 150 gm
DESIGN OF GEAR PAIR FOR WRIST ROLL
Design of Gear
The I.D. of the gear is 15 mm to suit the sleeve.
Assuming a module of 2 and dia of 60 (since it should be greater than the dia of the sleeve )
Hence no of teeth = Z = dia/mod -2
= 60/2 -2 =28
Z = 28 teeth
The width of gear is 20 mm
Design of pinion
Considering a speed reduction of 1:2
N1Z1= N2Z2
Z2 = Z1/3 because reduction is 1:2
Z2 = 28/2 = 14
The value of Z2 chosen is 13
Id of the mating gear is = to the shaft of the motor = 15 mm
The width of gear is 20 mm
To check for strength of tooth
Using Lewis form factor for involute system and 20 degree pressure angle we have
Y = 0.154 -0.912/z
= 0.154 -0.912/13
=0.0838
Using Lewis equation
Ft = s d x Cv x B x y x p x m
Where
Ft = tangential load on the gear (assume a maximum of 20 N)
s d = design stress of material = 20 N/mm3
Cv = velocity factor = 0.276 for ordinary cut gears
Y = Lewis form factor = 0.0838
M= module = 2
B = width of gear = 20 mm
= 20 x 0.276 x 20 x 0.0838 x 3.14 x2
=58N
Hence design is safe
DESIGN OF BALL BEARING
From the data sheets we can see that the load that the bearing will be subjected to is far less than the design load hence the need for further verification of design is unnecessary.
DESIGN OF BEARING HOUSING.
To avoid excessive machining and prevention of thin walls we can assume the following dimensions
MATERIAL =ALUMINIUM
LENGTH = 50mm
WIDTH = 50mm
HEIGHT= 45 mm
INNER DIAMETER OF HOLE= outer dia of the bearing = 32mm
DEPTH OF HOLE = 12 mm
APPROX WEIGHT = 300 gm
MOTOR TORQUE CALCULATIONS
Neglecting the mass moment of inertia of the rotating structure due to low velocities and zero acceleration . Assuming the load to act at the extreme end of the end effector is 900 grams.
The moment about the turning axis is =m x d
=0.900 x 0.6
=0.54 kg cm
No of teeth on wrist roll gear = 28
No of teeth on wrist roll pinion =13
The gear ratio is almost 1:2
Hence torque required to turn the structure = 1/2 x 0.54 =0.27 kg-cm
The motor selected is of torque 0.3 kg-cm hence design is safe.
SPECIFICATION OF THE WRIST ROLL
Material of wrist roll housing = aluminium
Length of wrist roll = 50 mm
Width of wrist = 50 mm
Height of wrist =45 mm
Bearings used =FLT ISKRA (POLAND)
No of bearings =3
Motor used =0.3Kg-cm motor
approx. weight(including bearings) = 600 grams
3) WRIST PITCH DESIGN
The wrist pitch is obtained by means of a worm gear pair. The worm gear is connected by means of a shaft to the C- clamp which in turn joins the wrist to the elbow.
SPECIFICATIONS OF THE C- CLAMP
Material = aluminium
Length = 80 mm
Breadth = 50 mm
Height = 12 mm
Approx. Weight = 130gms
Bearing housed =2 numbers
Total weight (approximate)=300gms
DESIGN OF WORM GEAR PAIR
The worm gear pair has the following specifications
Module = 1
No of teeth of worm wheel = 40
Dia of wheel = 42 mm
Face width = 20 mm
No of start of worm shaft = 2
Dia of worm shaft = 20 mm
Length of worm shaft = 75 mm
Approximate weight of the pair (including worm shaft housing)= 600 gms
Total load on the worm shaft = Wt of object + wt of gripper + wt of sleeve
+ wt of wrist roll assembly
+ wt of wrist roll motor + wt of wrist roll gears
=100 + 500 + 150 + 600 + 300 + 300 =1950 gm
=19.13 N say 20 N
The Lewis form factor is given by
y= 0.314 + 0.015(a -14.5° )
=0.314 + 0.015(29-14.5° )
=0.3965
The permissible tooth load is given by Lewis equation
Ft = s d x Cv x B x Y x M
Where
Ft = tangential load on the gear (assume a maximum of 25 N)
s d = design stress of material = 50 N/mm2
For the hylam worm shaft
Cv = velocity factor = 3.05/(3.05 +V)= 0.276 for ordinary cut gears for a velocity of 8m/s
Y = Lewis form factor = 0.3965
M= module = 1
B = width of gear = 20 mm
Ft = 50 x 0.276 x 20 x 0.396 x 1
= 109.3 N
since the maximum allowable is 109 N/mm2 and the applied load is 25N Hence design is safe with a f.o.s. of 5
SELECTION OF MOTOR FOR WRIST PITCH
In order to calculate the motor torque we calculate the weight till the wrist pitch and as a case of worst loading assume the load to act at the tip of the end effector. The weights are as follows:
1.Weight of the payload = 100 gm
2.Weight of the end effector = 500 gm
3.Weight of the end effector sleeve = 150 gm
4.Weight of the bearing housing = 600 gm
5.Weight of the gears for wrist roll = 300 gm
6.Weight of the wrist roll motor = 300 gm
7.Weight of the C-clamp = 130 gm
8.Weight of the wrist pitch worm pair = 600 gm
Total weight =2880 gm
Consider a safe load of 3000 gm =29.43 N
This load is acting at a distance :
1.Length of gripper = 176 mm
2.Length of sleeve projection = 10 mm
3.Length of bearing housing = 50 mm
4.Length of C- clamp clearance = 15 mm
Total length = 251 mm
The total torque exerted = force x distance
=3kg x 25 cms =75 kg-cms
Now a worm gear pair of reduction 1:40 is used
Hence load on the motor = 75 /40 = 1.875 kg-cms
The motor used is a 3 kg-cm motor
The motor is connected to the worm shaft by a 6mm dia tube of length = 275mm through a nipple of dia 20 mm and length = 35mm
The motor is housed with the help of 2 mild steel plates of dimension
100 x 30 x 2 mm which are welded onto the elbow.
4) DESIGN OF ELBOW
The elbow is designed as a cantilever beam with one end fixed and the other end free. The length of the elbow is taken to be 380mm.The elbow selected in the design is a mild steel box section of size 25mm x 25 mm. The total load on the elbow is taken from above and is =3 kg. The additional weight acting on it is:
1.The weight of the wrist pitch motor = 450gm
2.The nipple and connector shaft = 250 gm.
3.The self weight of the box section = 300
The total weight acting on the box section is = 4 kg. This weight is acting at a distance of 251 mm(up to the c-clamp) and the length of the elbow = 380 mm.
Hence, total weight acting 4 kg
Total distance =631 mm
The torque acting on the box section = force x distance
= 4 x 9.81 x 631 = 24760 N-mm
The stress on the member is given by s = M/Z
Where M is the bending moment or torque
Z is section modulus
We know that the torque acting is = 24760 N-mm
The section modulus is given by (BH3- bh3)/6H
Where
B=25 mm
H=25mm
b=23mm
h=23 mm
Z=(25 x 253 - 23 x 233) /6 x 25
Z=738.5 mm4
Hence the stress is 24760/738.4
s =33.53 N/mm2
The allowable shear stress s a for mild steel =200 N/mm2
Hence, the design is safe
Design of worm gear pair
The worm gear pair has the following specifications
1.Module = 2
2.Material of worm wheel = cast iron
3.No of teeth of worm wheel = 40
4.Dia of wheel = 85mm
5.Face width = 22 mm
6.Material of worm shaft = mild steel
7.No of starts of worm shaft = 1
8.Dia of worm shaft = 20 mm
9.Length of worm shaft = 95 mm
10.Approx weight of the pair (including worm shaft housing)= 800 gm
Total load on the worm shaft = is calculated from above and found to be 4 Kgs. = 4 x 9.81=39.24 » 40 N
The Lewis form factor is given by
y= 0.314 + 0.015(a -14.5° )
=0.314 + 0.015(29-14.5° )
=0.3965
The permissible tooth load is given by Lewis equation
Ft = s d x Cv x B x Y x m
Where
Ft = tangential load on the gear (assume a maximum of 40 N)
s d = design stress of material = 56 N/mm2
for the worm shaft
Cv = velocity factor = 3.05/(3.05 +V)= 0.276 for ordinary cut gears for a velocity of 8m/s
Y = Lewis form factor = 0.3965
M= module = 2
B = width of gear = 22 mm
s d = 56 x .276 x 22 x .396 x 2
s d = 269.3 N/mm2
Since the maximum allowable is 269N/mm2 and the applied load is 40N,Hence design is safe with a f.o.s. of 6
ELBOW MOTOR TORQUE CALCULATIONS
The elbow motor is to lift the torque of 24760 N-mm calculated above This is done with the help of a worm gear pair of reduction 1:40. Thus the actual load to be carried is = 24760/40 = 619 N-mm
Converting to Kg-cm, we have
619/10 x 9.81 = 6.3 Kg-cm
The motor used in our application is a 13 Kg-cm motor .The motor details are available in the appendix. The motor is connected to the worm pair by means of a connecting tube of dia 6 mm and length 250 mm, by means of a nipple of O.D 35 mm and length 20 mm.
The elbow is connected to the shoulder by means of a C-clamp of the following specification
1.Material = aluminium
2.Dimension = 50 x 50 x 12
3.Hole of O.D = 32 depth 10 mm to house the bearings
Note: during practical examination of the motor it was found that it did not produce sufficient torque when a payload was applied .As a result a counter weight of weight 1 Kg was attached at a length of 270 mm, to help increase the lifting capability. This was done by using a box section tube of dimension 12 x 12 mm
SPECIFICATION OF THE ELBOW
5) DESIGN OF THE SHOULDER
The Shoulder is designed as a cantilever beam with one end fixed and the other end free. The length of the shoulder is taken to be 410 mm. The Shoulder selected in the design is a mild steel box section of size 25 mm x 25 mm. The total load on the shoulder is taken from above and is =4 kg. The additional weight acting on it are:
1.The weight of the elbow motor = 1 kg
2.The nipple and connector shaft = 250 gm.
3.The self weight of the box section = 300gm
4. The weight of the C-clamp and bearings = 500 gm
5. Weight of counter weight and housing =1500 gm
The total weight acting on the box section is = 7.5 kg. This weight is acting at a distance of the elbow = 631 mm i.e. at the end of the elbow calculated from above and the length of shoulder = 450 mm
Hence total weight acting 7.5 kg
Total distance =1081 mm
The torque acting on the box section = force x distance
= 7.5 x 9.81 x 1081 = 79534.6 N-mm
The stress on the member is given by s = M/Z
Where M is the bending moment or torque
Z is section modulus
We know that the torque acting is = 61273 N-mm
The section modulus is given by (BH3- bh3)/6H
Where B=25 mm
H=25mm
b=23mm
h=23 mm
Z =(25 x 253 - 23 x 233) /6 x 25
Z=738.5 mm4
Hence the stress is 79534.6 /738.4
s =107.71 N/mm2
The allowable shear stress s a for mild steel =200 N/mm2
Hence the design is safe
DESIGN OF WORM GEAR PAIR
The worm gear pair have the following specifications
1.material of worm wheel = brass
2.Module = 2
3.No of teeth of worm wheel = 40
4.Dia of wheel = 85 mm
5.Face width = 22 mm
6.Material of worm shaft = mild steel
7.No of start of worm shaft = 2
8.Dia of worm shaft = 65 mm
9.Length of worm shaft = 50 mm
10.Approx weight of the pair = 1750 gm
Total load on the worm shaft = is calculated from above and found to be 7.5 Kgs.
= 7.5 x 9.81=73.57 » 75 N
the Lewis form factor is given by
Y = 0.314 + 0.015(a -14.5° )
=0. 314 + 0.015(29 -14.5° )
Y = 0.3965
The permissible tooth load is given by Lewis equation
Ft = s d x Cv x B x Y x m
Where
Ft = tangential load on the gear (assume a maximum of 60 N)
s d = design stress of material = 56 N/mm2
for the worm shaft
Cv = velocity factor = 3.05/(3.05 +V)= 0.276 for ordinary cut gears for a velocity of 8m/s
Y = Lewis form factor = 0.3965
M= module = 2
B = width of gear = 22 mm
s d = 56 x .276 x 22 x .396 x 2
s d = 269.3 N/mm2
Since the maximum allowable is 269N/mm2 and the applied load is 60 N. Hence design is safe with a f.o.s. of 3
SHOULDER MOTOR TORQUE CALCULATIONS
The Shoulder motor is to lift the torque of 63627.6 N-mm as calculated above. This is done with the help of a worm gear pair of reduction 1:40. Thus the actual load to be carried is = 79534.6 /40 = 1988.4
converting to Kg-cm we have
1988.4/10 x 9.81 = 20.26 Kg-cm
The motor used in our application is a 28 Kg-cm motor .The motor details are available in the appendix.
The motor is fixed onto the base by means of a mild steel plate. This plate is welded on the base and measures 85 x 20 x 5mm.
The Shoulder is connected to the base by means of a C-clamp of the following specification:
1.Material = aluminium
2.Dimension = 100 x 175 x 15(first plate )
3.Dimension = 100 x 140 x 15(second plate)
4.Hole of O.D. = 32, depth = 12 mm to house the bearings
Note: During practical examination of the motor it was found that it did not produce sufficient torque when a payload was applied. As a result a counter weight of weight 5.5 Kg was attached at the end of the shoulder.
Due space limitations a semi cylindrical vessel was made of radius 85 mm and height 45 mm. This was filled with lead which has a very high density of 11340 Kg/m3 to help increase the lifting capability. This was found inefficient and hence another weight of mass 3 Kgs was suspended from the worm wheel shaft by using a box section tube of dimension 12 x 12 mm.
DESIGN OF SHOULDER SHAFT
The shoulder is connected to the C-clamp mounted on the base by means of a stepped shaft. The outer dia suiting the inner dia of the worm shaft = 25 mm and the inner dia suiting the bearing of I.D. 15mm
Considering the least dia as 15 mm, the total load on the shaft is
7.5 kgs from above along with this it carries the counter weight of almost 8.5 Kg.
The total load on the shaft = 7.5 +8.5 = 16 kg = 157 N
The stress on the shaft can be calculated by considering the shaft as a simply supported beam with point load at the center.
s =M/Z
where M= bending moment = 1/2 x load x length of shaft
= 1/2 x 157 x 130
= 10205 N-mm
Z= section modulus = p d3/32 =p x 153/32
=331.33 mm3
s = 10205/331.33 = 30.8 N/mm2
The safe design stress for mild steel is 200 N/mm2
SPECIFICATION OF THE SHOULDER
1.Total length = 450 mm
2.Effective length = 430 mm
3.Section = box section = 25.4 x 25.4 mm
4.Shoulder motor 28 Kg-cm
5.Worm gear pair = 1:40 reduction
DESIGN OF BALL BEARING:
The ball bearing used in all the joints is the same and is FLT ISKRA
I.D. = 15 mm
O.D. = 32 mm
THICKNESS = 9mm
SUGGESTED RPM = 22000 rpm
STATIC LOAD CAPACITY = 255 Kg
DYNAMIC LOAD CAPACITY = 440 Kg
Thus we can say that if the bearing is safe for the shoulder it is safe for all other joints.
6) DESIGN OF BASE
The total weight acting on the base is 16 kgs apart from:
The total weight on the base is approx. =25 kgs.
DESIGN OF BASE SHAFT
The base shaft, which is stepped, has a dia varying from a minimum of 20 mm to a maximum of 25 mm. In order to check the strength of the shaft,
We apply the Rankines formula for a short column
s c = F/A[1+(l/k)2 s e/p 2nE]
Where
s c = critical stress induced
F= load applied = 25 x 9.81 = 245.2N
A = area of cross section of shaft =p d2/4 = p x 202/4 =314.14 mm2
l = length of the shaft = 175 mm
k = radius of gyration = d/2 = 10 mm
s e = tensile strength of material of shaft (mild steel) = 600 N/mm2
n = 1 for both ends fixed
E = modulus of elasticity = 1.9 x 105 N/mm2
s c = 245.5/314.14[1 +(175/10) 2 x 600/p 2 x 1 x 1.9 x 105]
= 0.85 N/mm2
Hence design is safe because allowable stress = 200 N/mm2
The base shaft is supported on a thrust bearing at the bottom of the shaft as well as a ball bearing for support at the top. The bearings are placed in bearing housings of dimension 75 x 75 x 12 for the thrust bearing and 75 x 70 x 12 for the ball bearing.
The specification of the bearing is as:
1) NACHI (Japan): Ball bearing
Code: 600422
Internal diameter: 20 mm
External diameter: 42 mm
Thickness: 12 mm
Suggested r.p.m : 17000
Static load capacity: 455 Kgs
Dynamic load capacity: 735 Kgs
2) ZKL (Czechoslovokia): Thrust ball bearing
Code: 51104
Internal diameter (Lower plate): 20 mm
Internal diameter (Upper plate): 21 mm
Internal diameter (Center plate): 20 mm
External diameter: 35 mm
Thickness: 10 mm
Suggested r.p.m: 5600
Static load capacity: 2200 Kgs
Dynamic load capacity: 1180 Kgs
From the specifications, it is evident that the bearing design is safe.
MOTOR TORQUE CALCULATIONS
The base is rotated using a 13 kg-cm motor through a spur gear pair with a reduction of 1:4
SPECIFICATION OF THE SPUR GEAR PAIR
It was found that the motor selected was working satisfactorily.
BASE STRUCTURE
The base has a fabricated structure made of mild steel box section of dimension 25 x 25 mm. This structure supports the entire arm of the robot. The final specifications of the base are:
1.Length = 190 mm
2.Width = 220 mm
3.Height = 170 mm
4.Semi circle radius = 100 mm
5.Motor = 13 Kg-cm
6.Gear pair = spur gear with 1:4 reduction
7.Base plate = O.D = 400mm thickness = 10 mm
8.Total weight of base = 4.5 kgs
A Note on the choice of stepper motors
The use of stepper motors was preferred by our group because they simplified our objectives considerably. Stepper motors give a rotation of 1.8 degrees per step. The number of steps fed into the motor can be easily controlled by using either a square wave generator or a desktop P.C. Hence the output of the motor can be easily controlled by the user. More steps are cumulative to the degree of rotation. This way costly and expensive feedback can be eliminated. Feedback, which is an integral part of any servo motor, has it’s own advantages and disadvantages. The advantage being its extremely high accuracy in pick and place operations. The disadvantage being the complicated mathematics and electronics that accompany feedback. This would have also escalated costs too considerably. Servo motors also do not suffer from the "slipping" effects that plague the stepper motor family. They also exhibit good speed –torque characteristics. The elimination of the use of servo motors by our group also eliminated the "force sensing and control" concept in our project . Hence by evaluating the cost factor and also keeping in mind the time limitations
Our group decided to use stepper motors which would serve our purposes adequately.