BTP Mid Report

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Pr. No.: D01

Design and Development of 6DoF Motion Platform

Submitted By:

Harshit Jain - 2009ME10072Praharsh Chandra2009ME10325

Supervisor:

Prof. S.K. Saha

Examiner:

Prof. J.K. Dutt

Mechanical Engineering Department

Indian Institute of Technology DelhiSeptember 2012


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CONTENTS

1. INTRODUCTION ........................................................................................................................ 12. LITERATURE REVIEW ............................................................................................................. 23. PROBLEM DEFINITION AND OBJECTIVES ......................................................................... 34. PROGRESS MADE ..................................................................................................................... 5

CAD Modeling ................................................................................................................................ 6Modeling on Autodesk Inventor ...................................................................................................... 6

5. WORK PLAN AND GANTT CHART........................................................................................ 8RERENCES ......................................................................................................................................... 9APPENDIX - A ................................................................................................................................. 10APPENDIX B .................................................................................................................................... 12

List of Figures

Figure 1: Stewart Platform ..................................................................................... 2Figure 2: Work Flow-Chart .................................................................................... 3Figure 3: Architecture of Top and Bottom Platform................................................. 5Figure 4: Few components including base plate, Hooke's joint, and slider ................ 6Figure 5: CAD models of few components.............................................................. 7Figure 6: Final Assembly ....................................................................................... 7Figure 7: Gantt Chart ...............................................Error! Bookmark not defined.
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upper parts through prismatic joints. The actuators may be of hydraulic piston-cylinder type or

electrical motor with precision ball-screw type [1].

The drivers cabin is attached to the upper platform which includes a screen on which the terrain is

projected thus giving the driver a real-life experience.

Figure 1: Stewart Platform

Following are some of the key terms associated with the project [1]:

Kinematics: For a parallel manipulator, it is defined as the study of the relationship between its

joints and the end-effector motions without referring to the cause of these motions.

Workspace: Workspace of a parallel manipulator is the space reachable by its end-effector.

Singularity: Singular configurations are those particular configurations of the end-effector, for

which a parallel robot loses its rigidity, and in which the end-effector will have uncontrollable

degrees of freedom.

2.LITERATURE REVIEW

The idea of the Stewart Platform design was first suggested by Eric Gough (1954) who devised a

six-jack layout. This was published by D Stewart in his 1965 paper to the UK Institution of

Mechanical Engineers.

Stewart (1965)[2] describes a mechanism, now called the Stewart Platform, having six degrees of

freedom and controlled in any combination by six motors, each having ground abutment. It

describes variations in control arrangements and their respective design merits while enumerating

the various advantages of using such a platform. The paper first suggested the possibility of using

the six link arrangement for simulating flight conditions in the training of pilots or for automation

of production.


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A lot work has been done since then covering the kinematics, dynamics and modeling of the

motion platform. Sadana (2009) [3] has attempted to develop an inverse dynamics model for

calculation of the actuation forces, required for real-time control. A method using Decoupled

Natural Orthogonal Complement (DeNOC) matrices has been developed which is utilized further to

derive a model for forward dynamics to perform simulations. Efforts to validate the model have

also been made by using CAD applications, I-deas and ADAMS. A GUI in MATLAB has been

developed which is being used in the current project.

Saha et al. (2009) [1] performed the mathematical modeling of the 6 DoF platform. This includes

kinematic and dynamic analysis of the platform. A workspace analysis has also been done taking

into account the actuators stroke, joint angle ranges and the leg interference constraints. Vehicles

response on some driving trajectory is considered and checked whether the platform is able to

achieve it or not.

Prathap (2012) [4] performed the modeling and simulation of 6-DoF Motion Platform using

CATIA DMU-Kinematics, which is a CAD simulation tool used to analyze the kinematic

behaviour of an assembly.

Introduction to Robotics by S.K. Saha (2008) [5] provides a simplified yet detailed explanation of

various concepts essential for the project. These include chapters on Actuators, Transformations,

Kinematics and Dynamics.

3.PROBLEM DEFINITION AND OBJECTIVES

The project is being developed for the Simulator Development Division of the Army. The various

problems to be solved during the design and development of the 6 DoF Motion Platform can be

summarised by the following flow chart:

Figure 2: Work Flow-Chart


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The present work pertains to the Mechanism Design, Analysis and Fabrication part and includes the

following objectives:

a)Designing of algorithms for 6-DOF Stewart Electrical Motion Platform based on

mathematical modeling - Mathematical modeling of the motion platform involves the study

of kinematics, dynamics, workspace and singularity analysis, and applying it for the control

of the motion platform. This part includes designing of various algorithms for the motion

platform.

b)Designing of motion base for 6-DOF Stewart Electrical Motion Platform based on

mathematical modeling - The second part contains detailed mechanical designing of the

motion platform. It starts with identification of COTS (Commercially off-the-self)

components for fabrication of 6-DOF Stewart Electrical Motion Platform and simulation of

final design. It also includes the engineering drawings, calculations, design specifications and

details of COTS components of the motion platform.

Following are the specifications for the 6-DOF Electric Motion Platform that is to be achieved.

These values have been used for designing the various components.

Specifications for the 6-DOF Electric Motion Platform:

1. Payload.

(a) Dynamic - 1000 Kg

(b) Static - 1200 Kg

2. Dynamics.

(a) Degree of freedom - 6

(i) Pitch (Front and back)

(ii) Roll (Right and left)(iii) Yaw (Clockwise and counter clockwise)

(iv) Surge (Forward and Reverse)

(v) Sway (Left and Right)

(vi) Heave (Up and Down)

(b) Pitch - 18

(c) Roll - 18

(d) Yaw - 18

(e) Surge - 20 cm


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(f) Sway - 20 cm

(g) Heave - 20 cm

3. Design Parameters.

(a) Closed height - 2 ft (~0.6 m)

(b) Operating height - 3 ft (~0.9 m)(c) Maximum height - 4 ft (~1.2 m)

(d) Frame size - 6 ft x 4 ft (~1.8 m x 1.2 m)

(e) Velocity - 20/sec

(f) Acceleration - 200/sec2

(g) Linear Velocity - 0.3 m/sec

(h) Linear Acceleration - 5 m/sec2

(i) Response - 25 ms

(j) Accuracy - 0.5 mm

4.PROGRESS MADE

Based on the reviews, the best architecture for top and bottom platforms was selected. Both the

platforms are semi-regular hexagons having their alternative sides parallel to each other. The frame

attachment and detail drawing is shown in fig 3, below.

Figure 3: Architecture of Top and Bottom Platform

cb: larger side of base platform = 1712mm; db: smaller side of base platform = 366mm;

ct: larger side of top platform = 910mm; dt = smaller side of top platform = 244mm.

The Y axis is perpendicular to the larger side of the bottom platform and to the smaller side of the

top platform.


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CAD Modeling

The next step was to develop a CAD model so as to study the kinematic behaviour of the Stewart

Platform. Using the Kinematic analysis by Saha et al. (2009), a MATLAB code was developed by

Mr Somyajit Roy, a PhD student from IIT Delhi, to determine the maximum and minimum leg

lengths, the details of which have been provided in Appendix A. The specifications defined in

section 3 above were used as input values in the code. The link lengths obtained were used to

develop a tentative model on Solidworks. F ig 4 depicts some of the components that were drawn.

However, it was found that with the above calculated actuators length, the full range of motion was

not achievable as the closing height and maximum height specifications were not met.

Hence, the maximum, operating and minimum heights were changed to obtain the full specified

workspace and to overcome the actuator stroke length constraint. The new heights taken for the

purpose were:

Maximum height =2.3m

Operating height = 1.65m

Minimum height = 1m

Using the above, the maximum and minimum leg lengths were found out to be as 241.51 cm and

125.83 cm respectively. (See Appendix A for further details)

Modeling on Autodesk Inventor

Autodesk inventor provides a better interface to analyze CAD models both kinematically and

dynamically. Hence, further designing was done on Autodesk Inventor rather than Solidworks. The

workings of Autodesk Inventor were learnt and all the components were redrawn on it.

Figure 4: Few components including base plate , Hooke's joint, and slider


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The dimensions of the various components were estimated using the basics of Mechanical Design,

the detailed analysis of which has been given in Appendix B.

Fig 5 shows some of the individual component CAD models that were drawn. The final assembly

is shown in Fig 6.

Figure 6: Final Assembly

Figure 5: CAD models of few components


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5.WORK PLAN AND GANTT CHART

SerialNo. Task Name Start Date

Duration(Days)

1 Study of related literature and understandingthe basics

01-08-2012 66

2 Design of Platform (various dimensions) 14-08-2012 23

3 Kinematic Analysis - Defining the workspace 05-09-2012 21

4 Learning software to perform FEA 26-09-2012 10

5 Stress analysis of various elements using FEA 03-10-2012 146 Singularity analysis 17-10-2012 14

Figure 7: Gantt Chart


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RERENCES

1.S.K. Saha, P.V.M. Rao and S. Bandopadhyay, Project Completion Report of Mathematical

Modeling of a 6- DoF Motion Platform, report submitted to SDD, April 2009.

2.Stewart, D. (1965), A platform with six degrees of freedom, Proc. Institution of Mechanical

Engineers, (Part-I), Vol. 180, No. 15, pp. 371-386

3.M. Sadana, Dynamic Analysis of 6 DOF Motion Platform, Department of Mechanical

Engineering, IIT Delhi, 2009

4.N. Prathap, Modeling and Simulation of 6 DOF Motion Platform using CATIA DMU-

Kinetics, Summer Report, SDD, Secunderabad, 2012

5.Saha, S.K. (2008), Introduction to Robotics, Tata Mcgraw Hill, New Delhi


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APPENDIX - A

Determination of Maximum and Minimum Leg Lengths

Based on the kinematic modeling, explained in section by Saha et al. (2009) a MATLAB code was

developed to compute the maximum and minimum leg lengths of the platform. Maximum,

operating and minimum height were changed (Maximum height =2.3m, Operating height = 1.65m

and Minimum height = 1m) to obtain the full specified workspace and to overcome the actuator

stroke length constraint. The inputs to this program were maximum and minimum pitch, roll, yaw,

surge, sway and heave values as per the specification given in section 2.3. Maximum and minimum

leg lengths are given in table 4.1.

Different

ConfigurationsSugre (cm) Sway (cm) Heave (cm) Pitch (deg) Roll (deg) Yaw (deg)

Maximum

Leg Length

(cm)

Minimum

Leg Length

(cm)

Closed height 0 0 100 0 0 0 124.55 124.55

Maximum height 0 0 230 0 0 0 241.69 241.69

Minimum heave

from operating

height

0 0 165-20 0 0 0 192.90 192.90

Maximum heave

from operating

height

0 0 165+20 0 0 0 199.34 199.34

Minimum surge

from operating

height

-20 0 165 0 0 0 189.94 173.78

Maximum surge

from operating

height

20 0 165 0 0 0 189.94 173.78

Minimum sway

from operating

height

0 -20 165 0 0 0 189.48 175.53

Maximum sway

from operating

height

0 20 1650 0 0

188.32 174.28

Minimum yaw

from operating

height

0 0 165 0 0 -18 189.41 175.01

Maximum yaw

from operating

height

0 0 165 0 0 18 189.41 175.01

Different

Configurations

Sugre (cm) Sway (cm) Heave (cm) Pitch (deg) Roll (deg) Yaw (deg)

Maximum

Leg Length

(cm)

Minimum

Leg Length

(cm)

Maximum pitch 0 0 165 18 0 0 193.10 164.52


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from operating

height

Minimum roll

from operating

height

0 0 165 0 -18 0 198.03 165.64

Maximum roll

from operating

height

0 0 0 0 18 0 198.03 165.64

In the next step, a particular configuration parameter was varied from its minimum to maximum

value while keeping other configuration parameters unchanged. This was done for all six of them.

The program was executed for different combinations of all configuration parameters to find out

the maximum and minimum leg lengths in its whole workspace and the orientation. Two different

configurations were obtained where the leg length is maximum compared to all other cases.

Similarly, another two different configurations were obtained where the leg length is minimum.

Different

ConfigurationsSugre (cm) Sway (cm) Heave (cm)

Pitch

(deg)

Roll

(deg)

Yaw

(deg)

Maximum

Leg Length

(cm)

Minimum

Leg Length

(cm)

Configuration 1

for maximum

leg length

-20 20 165+20 18 -18 18 241.51 184.14

Configuration 2

for maximum

leg length

20 20 165+20 18 18 -18 241.51 184.14

Configuration 1

for minimum

leg length

-6.7 20 165-20 -18 18 18 192.68 125.83

Configuration 2

for minimum

leg length

6.7 20 165-20 -18 -18 -18 192.68 125.83

So, the maximum leg length = 241.51cm and the minimum leg length = 125.83cm were selected.


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APPENDIX B

MECHANICAL DESIGN

1. Lead Screw

The main rotating component of the actuator is lead screw. It is a part of lower leg. As the nut is

unable to rotate, the helical threads on lead screw compel the nut to advance along its axis.

Generally square thread is used in lead screws, but as trapezoidal thread is easy to manufacture here

trapezoidal or ACME thread was preferred. The lead screw is rotated by a servo motor, via a

suitable gear box.

The material for the lead screw was as C50 hardened hot rolled steel whose yield stress is 340

N/mm2. Taking Factor of Safety (FOS) as 2 the core diameter, d c was calculated by compressive

stress analysis as

(B.1)Where, F = 8012.5 N, Syt = 340 N/mm

2 and FOS = 2. Equation (5.1) yields, dc=7.75mm.

Considering pitch, p = 1.5mm, nominal clearance = 0.15 mm, height h = 0.5 p + nominalclearance = 0.9mm, the nominal diameter was obtained as d=dc+2h=9.55mm. Hence, the next

available diameter available is 10mm with pitch 2 mm and core whose diameter 8mm. Note that the

lead screw must not buckle. Hence, checking for buckling was done. The end-conditions were

taken as hinged-hinged. Effective length was taken equal to the original length of the screw, i.e.,

Leff= 2415.1mm. We know,

(B.2)where E is the modulus of elasticity, I is the section modulus and Leff is effective length.

Calculating, I = = = 201.062mm2; (B.3)

and taking E=210 GPa from, Pcr was obtained as 71.44 N, which is less than 8012.5 N. So the

screw fails in buckling. Hence, considering buckling, the core diameter was recalculated as dc =

25.79mm. Taking the next available diameter, dc = 26mm, other parameters were obtained as, d =

32mm, p = 6mm, and diameter, dm = 29mm. The lead screw to be used in the 6-DOF motion

platform is shown in Fig. B.1.

Now, the torque required to lift the pay load is calculated below:

Thread angle 2 = 30o Torque required to lift the load, T=

(B.4)


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where W: load lifted, : coefficient of friction between nut and screw = 0.125, : threadangle, and : helix angle =

From Equation (B.4), T = 22881.55 N.mm

Now the stresses are calculated as

Compressive stress, N/mm2 Shear stress, N/mm2

Maximum principle stress , = 17.59 N/mm2

Maximum shear stress, = 10.05 N/mm2

Since and are less than Syt (340 N/mm2) and (170 N/mm2), the design is safe.

Fig. B.1 Lead screw

2. Nut with Anti-rotation cum Guide Bar Collar

The nut has suitable internal thread mating with the lead screw. The rotation of the nut is blocked

by a guide bar collar which is situated just above the nut. The collar has two holes through which

two fixed studs are made to pass. This ensures movement of the nut without rotation. The nut is

attached to the upper leg cylinder. As the nut gets translatory movement, the upper leg also moves

in a linear motion.

The material of the nut is taken as Phosphorus bronze. It was designed for bearing pressure to find

the length of engaged threads. Then, shear stress on the thread root was checked.

Number of threads engaged with lead screw, z =

=19.54 Where Sb for bronze and steel for high speed (>15 m/min) was taken as 1.5 N/mm

2

Length of nut = 20 x 6 = 120 mm


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Next,

Shear stress on screw, ,= 1.63 N/mm2

Where, t: root thickness of thread = p/2 = 3mm.

Shear stress on nut, = 1.33 N/mm2 The designed nut is shown in Fig. B.2

Fig. B.2 Nut with anti-rotating collar

3. Gear box

Gears are used to transmit power from motor to lead screw. Depending upon the motor and the

center distance between the motor and lead screw, the gear ratio was selected.

Before the gear box was selected, it was necessary to find the power to be transmitted. For that,

Torque required, T = 22881.553 N.mm

Sliding velocity = 363.4 mm/sec

Rotation of screw =

rev/sec = 60.57 rev/sec Angular velocity of lead screw, rad/sec Power, P = T = 8.707 kW

It is necessary that the above power is to be transmitted by each gear box attached to the legs. The

calculations for the pinion were done using the following steps. Material: Plain carbon steel 40C8


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Ultimate tensile strength, Sut = 600 N/mm2

Start with minimum number of teeth, zp = 18 for 20o pressure angle gear.

Module, m =

Where, P: power rating in kilowatt, Cs: service factor = 1 (since driver and driven both are

uniform.), Cv: velocity factor =

(assuming pitch line velocity 5 m/sec), FOS:factor of safety = 1.5, zp = number of teeth, np = revolution per minute, b = face width, Y:

Lewis form factor = 0.308 (for number of teeth = 18), and .

Pitch circle diameter, dp = mzp = 3 mm, b = 10 3 = 30mmNow, to check the selected pinion parameters, following calculations were carried out:

Force on teeth, Pt = Velocity, v =

= 10.27 m/sec

For velocity greater than 10 m/sec C v =

Effective load on teeth, Peff =

Strength of teeth, Sb = mb Factor of safety, FOS =

Since FOS is greater than 1, the pinion is safe which is shown in Fig.B.3.

Fig: B.3 Pinion


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4. Spider for Universal Joint

This is actually a cross arm structure having four legs of equal diameter and length. Each coupling

is attached to its opposite pair of legs.

The following steps were taken to design the spider:

Material: C50 hardened hot rolled steel.

Yield stress, Syt = 340 N/mm2.

Factor of safety FOS = 2. (assumed)

Total load, W = 8012.5 N

Moment, M = 8012.5 x 50 N.mm = 400625 N.mm

Stress due to moment, , which yields the diameter of the spider, d = 29mm. Shear stress,

N/mm2

is less than the corresponding yield strength. Hence, the spider is safe, which is shown in Fig.B.4.

Fig. B.4 Spider for universal joint

5. Coupling for Universal Joint

Couplings are provided to assemble the joints. There are six universal and six spherical joints.

Universal joints are made by two intersecting revolute joint axes whereas the spherical joints are

made by three intersecting revolute joint axes.

The design steps for the coupling are as follows:



Factor of safety, FOS = 2.

Coupling dimensions are shown in Fig. B.5.


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Compressive stress, N/mm2. Bearing pressure, N/mm2.

Since, and both are less than Syt (340 N/mm2), the design is safe, which is shown in Fig B.5.

Fig. B.5 Coupling for universal joint

6. Connector

It connects the gear box assembly to the universal joint. The design steps for connector are as

follows:



Factor of safety, FOS = 2.

Dimensions of connector, as shown in Fig. B.6, were chosen according to fit with other

components.

Compressive stress,

N/mm2.Since less than compressive strength, i.e., Syt = 340 N/mm2, the design is safe. (See fig B.6)


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Fig. B.6 Connector

7. Moving tube and fixed tube

Moving actuator tube is attached to nut. As the nut moves the tube goes upward and gives motionto the top platform. Fixed tube surrounds the lead screw and provides space for the moving tube.

The moving tube has to withstand the total load. Dimensions of the tube are chosen according to fit

with other components, as shown in Fig. B.7. The tube was then checked for failure, as per the

following calculations.

Compressive stress, N/mm2 End condition: fixed-hinged.

Effective length, Leff = 0.7L

Area moment of inertia, I = mm4

Critical load for buckling, Pcr = 947826.78 N.

Since Pcr is less than the applied load 8012.5 N, the design is safe.


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Fig. B.7 Moving tube

8. Nut stopper

It stops the movement of the nut after maximum height is reached. Dimensions of the nut stopper

are chosen according to fit with other components, as shown in Fig. B.8

Fig. B.8 Nut stopper

9. Stud

Two studs are provided to stop rotation of the nut. They pass through the hole provided in the anti-

rotation collar of the nut and secure only translation movement of the nut. Dimensions of stud is

shown in Fig. B.9

Fig. B.9 Stud

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