Mechatronics System Design 
Department of Mechanical & Industrial Engineering
MEC830 Mechatronics System Design
Final Report – Team Legotron
Program: Mechanical Engineering
Due Date: April 8, 2008
Prepared for:
Prof. F. Sharifi
Names Hector Cueva Jugal Parikh Kerry Thakurdin Samir Jariwala
Student ID XXX108012 XXX993745 XXX734013 XXX391741
ACKNOWLEDGEMENTS
The design team, Team Legotron, would like to acknowledge and extend their gratitude to the following persons who have made the completion of this project possible: Our professor, Professor Farrokh Sharifi, for his commitment to our class and our project through the teaching of core concepts, providing the required resources, and his continued guidance and support. Mr. Devin Ostrom, Technical Officer, for his continued efforts to teach and guide our class throughout our project. Without his efforts to constantly provide technical assistance, supervision and technical guidance, this project could not have been completed. Mr. Senthilnathan Panchatsaram, for his guidance and supervision during the labs, and his selfless act to provide us with additional time to ensure that the all the design teams had sufficient time in the lab to complete the project. Lastly, Legotron acknowledge and thank to the entire Mechanical Engineering Department at Ryerson University for their continued support of our class, the Mechatronics stream and the entire Engineering student body.
EXECUTIVE SUMMARY
The continued developments in robotics have an astounding potential to change and improve our quality of life. Robots are heavily used in the industrial and medical industries, and are The stemming into several new areas. The advantage of using multiple robots to perform a given task is the intended emphasis of the project presented to the Legotron design team. unison with the Mecbot to complete an outlined course. The proposed course poses many challenges; as a result, several design parameters for the design of the robot were continuously developed. Several prototypes of the robot were built; each successive prototype was built to rectify any problems encountered by the preceding model. The simulation of the mechanical system is obtained by using SimMechanics which allows the designer to manipulate design parameters and their effects on the overall assembly. Conceptual design of the robot is further understood through the functional requirements which are derived from the design matrices and design parameters. The build, design and programming of the Lego robot were successful. The robot performed as required, successfully traveling through the course. Challenges were encountered such as electrical complications (light sensors) and mechanical challenges, in particular when turning. The mechanical challenges caused the robot to slightly deviate from the desired path and increase the time required when turning due to the excessive amount of friction form the equipped wheels. Reinforcing the rear axis to avoid any deformation of the wheel axis could minimize the turning radius and in return, reduce the time required to complete the turns. More successful and consistent turning may also be achieved by using the tracks as the primary turning mechanism; this would reduce the amount of deformation on the axis and substantially limit the friction encountered between the wheels and the travelling surface; resulting once again in the reduction of the turning radius and turning time. proposed project involves designing, building and programming a Lego robot to function in
TABLE OF CONTENTS
1 2 INTRODUCTION .................................................................................................................. 5 THEORETICAL BACKGROUND ........................................................................................ 7 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 3 Input Ports ....................................................................................................................... 7 Output Ports .................................................................................................................... 7 Buttons ............................................................................................................................ 7 IR Tower ......................................................................................................................... 9 Motor............................................................................................................................... 9 Sensors .......................................................................................................................... 12 Gears Ratio.................................................................................................................... 13 Torque ........................................................................................................................... 13 Speed ............................................................................................................................. 14 Force ............................................................................................................................. 14 PWM and Motor Speed ................................................................................................ 15
MODELING ......................................................................................................................... 16 3.1 Product Architecture Schematic (PAS) ........................................................................ 16 3.2 Conceptual .................................................................................................................... 17 3.3 Mechanical .................................................................................................................... 21 3.3.1 Dynamic Analysis ................................................................................................. 21 3.3.2 Stall Torque of the Two DC Motors ..................................................................... 22 3.4 Control .......................................................................................................................... 23 3.5 Sensory.......................................................................................................................... 24
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DESIGN AND OPTIMIZATION......................................................................................... 25 4.1 Conceptual .................................................................................................................... 25 4.1.1 Requirement Phase................................................................................................ 25 4.2 Specification Phase ....................................................................................................... 26 4.2.1 Power System........................................................................................................ 26 4.2.2 Design ................................................................................................................... 26 4.2.3 Design of Mechanism: .......................................................................................... 27 4.3 Integration ..................................................................................................................... 27 4.3.1 Virtual Prototyping: .............................................................................................. 27 4.3.2 Physical Realization:............................................................................................. 27 4.3.3 Operation............................................................................................................... 28 4.4 Mechanical .................................................................................................................... 28 4.4.1 Mechanical System ............................................................................................... 28 4.4.2 Relation of Power System to Mechanical System ................................................ 28 4.5 Control .......................................................................................................................... 28 4.5.1 Control System...................................................................................................... 28 4.5.2 Relation of Power System to Control System....................................................... 29 4.6 Sensory.......................................................................................................................... 29 4.6.1 Sensor System ....................................................................................................... 29
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4.6.2 4.6.3 4.6.4 5
Relation of Power System to Sensor System ........................................................ 29 Relation of Mechanical System to Sensor System ............................................... 30 Relation of Control System to Sensor System ...................................................... 30
IMPLEMENTATION ISSUES AND EXPERIMENTAL RESULTS VERSUS
SIMULATION RESULTS ........................................................................................................... 31 6 7 DISCUSSION AND CONCLUSION................................................................................... 33 REFERENCES ..................................................................................................................... 34
APPENDIX A - ANALYSIS OF STALL TORQUE ............................................................... A - 1 APPENDIX B – PART LOAD COUNTER, VELOCITY SENSOR & WEIGHT SENSOR . A - 1 APPENDIX C – C Programming ............................................................................................. A - 1
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LIST OF FIGURES
Figure 1: Representation of the Course ......................................................................................... 5 Figure 2: RCX Brick with Inputs and Outputs[1] ........................................................................... 8 Figure 3: IR Tower[2] ..................................................................................................................... 9 Figure 4: 9 V RCX Motor[2] .......................................................................................................... 9 Figure 5: Circuit Model of DC Motor[7] ...................................................................................... 10 Figure 6: Block Diagram of DC motor[8] .................................................................................... 10 Figure 7: 3:1 Gear Ratio .............................................................................................................. 13 Figure 8: Ratio of Torque is Equal to the Ratio of the Radii ....................................................... 14 Figure 9: Ratio of Rotation Speed is Equal to Inverse of Radii................................................... 14 Figure 10: Force, Torque and Radius Relationship for a Wheel ................................................. 15 Figure 11: PWM Duty Cycle ....................................................................................................... 15 Figure 12: Product Architecture Schematic (PAS) ....................................................................... 16 Figure 13: Space Rover Vehicle Design[3] .................................................................................. 17 Figure 14: Concept Link Design ................................................................................................... 18 Figure 15: Lego Link Design Model ............................................................................................ 19 Figure 16: RoboWorks Model of Link Design ............................................................................. 19 Figure 17: SimMechanics Block Diagram of Link Design .......................................................... 20 Figure 18: FBD of Stair Case and Front Wheel ............................................................................ 21 Figure 19: Bang-bang Algorithm Flowchart................................................................................. 23 Figure 20: Light Sensor Calibration ............................................................................................. 24 Figure 21: Lego Robot and Mecbot Hierarchy Diagram .............................................................. 25 Figure 22: Implementation of Improved Design Parameters ........................................................ 31 Figure A 1: Figure A 2: Figure A 3: Figure A 4: Torque vs Speed for Motor 1................................................................................ A - 2 Torque vs Speed for Motor 2................................................................................ A - 2 Max Power Motor 1.............................................................................................. A - 3 Max Power Motor 2.............................................................................................. A - 3
Figure B 1: Load Sensor Mechanism....................................................................................... B - 3
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LIST OF TABLES
Table 1: Simulink DC Motor Model............................................................................................. 11 Table 2: DC Motor Steady State Speed Response ........................................................................ 11 Table 3: RCX Sensors[2] .............................................................................................................. 12 Table 4: VR Model of Link Design Frame by Frame .................................................................. 21 Table 5: Stall Torque Experimental Observations ....................................................................... 22 Table 6: Power Observation for Stall Torque .............................................................................. 23 Table B 1: Experimental Observations .................................................................................... B - 3 Table B 2: Linear Relationship between IR Reading and Load .............................................. B - 4
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1
INTRODUCTION
Team Legotron was asked to produce a prototype Lego mobile robot, using the Lego Mindstorm kit that will perform in unison with the Mecbot, to complete the proposed course. The course is intended to emphasize the advantages of using multiple robots to perform a given a task. To understand the performance and the design parameters required of the Lego mobile robot, the first step was to understand the challenges the course presented. The Lego robot must first climb up and over a set of stairs. Using only sensors to navigate the robot, it must travel along the encountered wall. The Ryerson mobile robot (Mecbot) is then waiting behind the wall for the Lego robot to come into contact with its bumper switches to initiate its travel. The Mecbot then travels along a strip of tape, using only the edge detector, until the course is completed.
Figure 1: Representation of the Course
The greatest initial challenge is the climbing and descending of the stairs. For this to occur, a high amount of torque is required in relation to the size and mechanics of the robot’s design. By analyzing the stall torques prior to building of the robot, an estimation of the motor’s performance limitations could be derived. In addition, the performance of the team’s initial
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design was analyzed in SimMechanics to further identify how the prototype was performing and what design parameter needed to be altered to enhance the current level of performance. To navigate around the wall, the Lego robot had to be mounted with light sensors. The sensors were programmed, in interactive C, to help control the navigation of the robot, with reference to the wall. How the robot would turn, when it would turn, and the various required speeds were developed through the software and the necessary mechanical modifications were applied as required. The Mecbot was programmed, also in interactive C, to follow the tape using the edge detectors. The initiation of the Mecbot was a significant challenge. To initiate the Mecbot the Lego robot had to successfully travel around the wall, without a significant amount of deviation in order to be in line with the bumper switch, which when contacted, initiates the travel of the Mecbot.
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2
THEORETICAL BACKGROUND
At first glance, the Lego Mindstorm kit may appear as nothing more than a toy, but for engineering students, inventors, and industries, it is a practical learning tool for prototyping devices. At the core of the RCX brick is a Hitachi H8 microcontroller with 32K of external RAM. RCX Lego Mindstorm model includes a programmable microcontroller-based brick that can simultaneously controls three motors, three sensors, and an infrared serial communication port.
2.1 Input Ports
The RCX brick contains three input ports that can accept a variety of Lego Sensors such as touch sensors, light sensors, and encoders. For the ease of connection, the connecting wire has both ends integrated with mountable Lego pieces, with metallic connections to the underside, providing easily mounting onto brick input ports. Also of significance, is that it is designed in such a way that the orientation of the connected Lego piece does not matter.
2.2 Output Ports
There are also three output ports that controls actuators, but mainly used for motors in this project. Unlike input ports, output ports behave differently for different orientation in which the motor is connected. When the wire is connected at the 6 o’clock or 9 o’clock orientation, the motor will turn clockwise conversely when the wire is connected at the 12 o’clock or 3 o’clock the motor will turn counter clockwise. However, this is only true when the motor end of the wire is connected such that it passes through the grove on motor. This encourages building model in symmetric pattern so that wheels rotation of a car are in same direction.
2.3 Buttons
There are four buttons on the RCX brick: On-Off, Run, View, and Pram. These allow the user to interact with the microcontroller, mostly to execute the downloaded program and built in firmware programs.
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On-Off: The main function of this button is to turn the power on or off. Notice that turning off the power does not erase the saved program. Run: This button starts executing the desired program. It also interrupts the program if pressed while the program is running. View: As a default the view button is programmed in firmware to show the value of the input and output ports. Pram: RCX is capable of storing five different programs. The Pram button is used to switch between programs and then executed using Run button.
Figure 2: RCX Brick with Inputs and Outputs[1]
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2.4 IR Tower
The Lego Mindstorm kit comes with an infrared transmitting tower. It allows the user to transfer the C program, developed on a PC, wirelessly to the brick. The IR signal transfer between IR tower and brick behaves much like a television remote control. The IR tower is connected to a PC via a serial port.
Figure 3: IR Tower[2]
2.5 Motor
The Lego Mindstorm kit comes with a 9-volt DC motor which runs on RCX AA battery pack or an AC adapter connected to the brick. Unfortunately, theses motors only have one rate of rotation. The speed of rotation can be decreased by supplying less voltage using firmware code, but there will be no change in the output torque. The only way to manipulate speed and torque is to use gears on output shafts.
Figure 4: 9 V RCX Motor[2]
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Figure 5 is a circuit model of the field control DC motor.
Figure 5: Circuit Model of DC Motor[7]
Using the electrical and mechanical system boundary analysis, the transfer function for the DC motor can easily be obtained. This transfer function is shown in Figure 6.
Figure 6: Block Diagram of DC motor[8]
Using the transfer function and the Simulink, the motors performances were observed. Table 1 shows the block diagam in Simulink, and motor parameters used.
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Table 1: Simulink DC Motor Model
DC Motor Block Diagram
DC motor Parameters
Finally, the motor speed output was obtained and displayed in Table 2. From the results it was evident that motor1 had higher speed than motor2. Hence, it was important to componset this difference in our programming.
Table 2: DC Motor Steady State Speed Response
DC Motor1 Steady State Speed Response ω = 32.5
DC Motor2 Steady State Speed Response ω = 33.2
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2.6 Sensors
Sensors are very important components of any robot, because they convey the information of the external surroundings. This information is then used to make a decision on what the next move should be. The Lego Mindstorm kit comes with different types of sensors, which include: touch sensors, light sensors and encoders.
Table 3: RCX Sensors[2]
Touch Sensor
Light Sensor
Encoder
Touch Sensors: It is the most basic and the easiest to program sensor in the RCX. It is typically used in conjunction with a bumper to detect the contact. It has only two states: on and off. Both on and off states are associated with Boolean logic true and false (i.e. 1 or 0). Light Sensors: The light sensors works on the light intensity. These sensors are mainly used to measure the distance between the object and the robot. Utilizing a C program, these sensors can detect the continuous wall and direct the robot to follow the wall without collision. Encoders: Encoders are used to measure how far a rotating axle has turned. It has a free spinning bushing which fits on a shaft and rotates as the shaft rotates. As the bushing turns, a counter in the RCX is incremented or decremented. Using the proper gear ratio and the radius of the wheels, the linear distance can be measured.
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2.7 Gears Ratio
Gear ratio is how much the output shaft turns for a given rotation of the input shaft. In Figure 7, we have an 8t gear pinion and a 24t output gear. If the 8t gear rotates one full revolution then eight of its teeth would pass through the starting line and 24t gear’s teeth also pass the starting line. If teeth are properly meshed and evenly distributed around the circumference of the gears, 24t gear turns 8/24 or 1/3 of a revolution. Hence, the gear ratio is given by the inverse of the ratio of the number of gear teeth, resulting in the following gear ratio: Gear Ratio = 1:1/3 = 3:1.
Figure 7: 3:1 Gear Ratio
2.8 Torque
Torque is the measure of a force's tendency to produce torsion and rotation about an axis. A typical example of a torque application is the required force to the turn the handle of a wrench. Gears operate by transmitting force at the teeth of the gear. In Figure 8, the torque transmission between two gears is displayed. Note that force experience by both gears is same. It also shows the relationship between the torques and the radii of the gears (number of teeth can also be used instead of radius).
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Figure 8: Ratio of Torque is Equal to the Ratio of the Radii
2.9 Speed
Gears are used to increase the output torque, but the speed is sacrificed in doing so. In essence, the output shaft turns stronger which allows it to increase load capacity of the machine but the shaft turns at a much slower rate. Figure 9, indicates the speed transfer between two gears. Note that this time linear velocity (tangential speed) of both gears is the same. This time the larger gear turns slower than the smaller.
Figure 9: Ratio of Rotation Speed is Equal to Inverse of Radii
2.10 Force
As established above, the relationship between force, torque and radius also holds true for a wheel. As shown in Figure 10, large wheels have a bigger radius (lever length) and will generate less force for a given torque than small wheels would. Less force means less acceleration. The car will go faster, but it will take longer to reach that speed.
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Torque
Wheel Torque = Motor Torque x Gear ratio Force = Wheel Torque / Radius
R Force
Figure 10: Force, Torque and Radius Relationship for a Wheel
2.11 PWM and Motor Speed
Pulse Width Modulation (PWM) provides a variable voltage supply to the motor by changing high and low at a fixed frequency. In Figure 11, duty cycle is the percentage of high period t versus total period T. DC = (t/T) x 100 %, where T fixed, and t varying.
t
T
Figure 11: PWM Duty Cycle
The RXC quickly switches the power on and off. Different power levels are achieved by varying the percentage of time that the power is on (this is called the duty cycle).
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3
MODELING
Modeling and simulation is a very important aspect of Mechatronics engineering. It allows engineers/designers to evaluate the entire system without physically building and implementing the design. More importantly, it allows to change and manipulate the design variables and to examine the effects on the resulting outputs. Modeling Mechatronics design problems include conceptual, mechanical, control and sensory design.
3.1 Product Architecture Schematic (PAS)
COMPUTER MOTORS POWER FRAME BATTERIES BODY (LEGO PIECES, WHEELS, ETC.) SENSORS BODY (LEGO PIECES, WHEELS, ETC.) STAIRS CLIMBING & ACTUATING ROBOT MCU GEARS
Figure 12: Product Architecture Schematic (PAS)
The Computer acts as the brain of both robots since it is used to program them. The computer provides both robots with instructions for the course and hence there is only information transfer
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between MCU and the Computer. The MCU passes the instructions to the motors, which in turn pass them onto the gears. Any sort of movement from the gears is directly translated into movement by the robot and hence the gears are one of the outputs of the system. Therefore the transfer / interaction between MCU and the motor, and the motor and gears are informational. Electrical components such as MCU, computer, and the sensors, need power to operate. The power supplied by electrical outlets and batteries and any kind of interaction between these components is energy transfer. For the Lego pieces used in the robot, there is a mass transfer through the body of the Lego Robot (or the frame). There is no change in what is being transferred, i.e. the robot at the beginning is same as the robot at the end. The robot moves from one end to another.
3.2 Conceptual
The concept of our initial design chassis originated from the space rover vehicle design shown in Figure 13.
Figure 13: Space Rover Vehicle Design[3]
Once the idea was generated concept sketch was developed as shown in Figure 14. Note that the center wheel is connected to the back frame and the front frame is free to rotate about the axis of 17
the link joint. It shows the robot in motion (to the left) climbing the stairs. As the front wheels come in contact with the vertical wall of the first step, the front link rotates upward as long as the center wheel does not touch the step. At this particular instant, front wheel catches the edge of the first step and the friction generates enough torque to pull center wheel over the first step. During all this time the back wheels are continuously pushing the whole car to move forward. This entire process continues until top of the stair. Coming down the floor is not a problem as gravity, in addition to the torque generated from motors, helps to drive the car down.
Figure 14: Concept Link Design
The main difference between the space rover design and our design is that our chassis had five wheels instead of six as shown in Figure 15. We eliminated one wheel from the center so that we can reduce the amount of space occupied by the extra wheel. In addition, due to the limitation of the numbers of motors available, and the high level of torque required, we were unable to utilize a steering based turning system. To tackle this issue, the back wheels were driven independently. As a result, to turn right, the left wheel was programmed to go forward
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while right wheel was programmed to go backward. Similarly, to turn left, the right wheel was programmed to go forward and left wheel was programmed to go backward.
Figure 15: Lego Link Design Model
Once the concept is developed and agreed upon, the next step is to model the concept using interactive modeling software such as RoboWorks and SimMechanics. RoboWorks is an easy to use software tool for 3D modeling, simulation and animation of any physical system. Figure 16, shows a working model of the concept. It can be animated so that viewer can see the actual rotation of the links and wheel as it climbs the stairs.
Figure 16: RoboWorks Model of Link Design
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SimMechanics is an extension to Simulink which helps modeling and simulating mechanical system with the construction of block diagrams. It allows designers to manipulate with design parameters and view their effects on the overall design. One of the major advantages of using SimMechanics over Simulink is that it does not require any transfer function. User can directly insert the mechanism in the form of blocks diagrams such as rigid body, joints, actuators, and sensors. Furthermore, it can also generate a 3D model and simulate with the Virtual Reality function.
Figure 17: SimMechanics Block Diagram of Link Design
As mentioned above, the build in Virtual Reality funsction was used to create the 3D model, and the simulation was created which is shown in Table 4. The SimMechanics model was created to simulate the motion at the instance where the robot begins to climb the stairs. The model was created in Solidworks and then imported into MATLAB. The force and velocity of the robot were analyzed. The simulation did not produce the desired results, which in this case is the robot climbing and descending the stairs. The simulation only involved the motion of front wheels moving up and down; the back wheels had no motion.
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Table 4: VR Model of Link Design Frame by Frame
Simulation Frame 1
Simulation Frame 2
Simulation Frame 3
3.3 Mechanical
Mechanical design is an essential part of Mechatronics system design. For the project, the analysis of speed, torque, friction, and inertia are all part of the mechanical design.
3.3.1 Dynamic Analysis
The most critical and challenging part of this project was to climb a stair case with the step height (55.0mm) is greater than the radius (40.8mm) of the biggest wheel from RCX MINDSTORMS kit. Hence, in-depth dynamic analysis had to be conducted to understand and improvise the design. Figure 18 is the FBD of the stair case and front wheel of the robot.
Figure 18: FBD of Stair Case and Front Wheel
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∑y=0= f
a= a=
A
− fB = 0
0 = μ A ma − μ B mg
μB g μA
0.3 (9.81) 0.4 a = 7.35m / s 2
From the static equilibrium in y direction, it is clear that if the acceleration of the carth is more than 7.35 m/s2. Note that the coefficients of friction are estimate values.
τA = μ A ma γ τ A = γμ A m a
fA = = (4.08 × 10 −3 )(0.4)(0.4)(7.35) τ A = 0.047 N • m
Finally, the torque required is calculated to be 0.047 N.m, which is substantially more than Tmax in Table 5. Hence, the gear ratio had to be utilized to provide sufficient torque in order to go over stair case.
3.3.2 Stall Torque of the Two DC Motors
The stall torque of the two DC motors is an essential analysis to understand the torque capabilities of the motors. This design parameter was analyzed by constructing a small structure that is capable of withstanding a significant amount of weight. The DC motors are mounted onto this structure, and the known mass is applied to the attached armature. By measuring the distance of the armature and recording the masses to achieve the stop torque for both motors, the stall torque can be derived.
Table 5: Stall Torque Experimental Observations
ωn
(rad/s)
ωn/2
(rad/s)
Load (g) 0.225 kg 0.250 kg
Motor 1 Motor 2
32.5 rad/s 33.2 rad/s
16.25 rad/s 16.6 rad/s
Kt (Nm/A) 0.277 0.271
U (V) 9.00 V 9.00 V
Ts (Nm) 0.044 Nm 0.049 Nm
Tmax (Nm) 0.022 Nm 0.0245 Nm
R (Ω) 56.7 Ω 49.8 Ω
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Table 6: Power Observation for Stall Torque
Pmax
Mechanical
Pmax
Electrical
Motor 1 Motor 2
0.358 W 0.407 W
0.90 W 0.90 W
*Refer to Appendix A for experimental parameters and sample calculations
3.4 Control
Many control methods such as bang-bang control, proportional control, proportional derivative control and proportion integral derivative control can be applied to this project. Most importantly, when the robot requires to turn and to follow the wall, the control is necessary to ensure that the robot follows the required path with minimum error. The simplest of all, bangbang control was used in this project. It adjusts the control only by two limits, min and max. It follows a simple algorithm, as shown in Figure 19; if the measurement is less than set point go to max else go to min. The set point, max and min are user defined.
Figure 19: Bang-bang Algorithm Flowchart
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3.5 Sensory
The touch sensor is a digital sensor with two states: 0 and 1. When sensor is pressed (actuated), the returned value is 1 and when it is released (not actuated) the returned value is 0. The light sensor used for this project is an analog sensor. Hence, the value measured by sensors is in analog and had to be converted into digital form. Also, the calibration is needed to establish a relationship between ADC reading and measurement value. The calibration plot for both light sensors is shown in Figure 20. According to the values, both sensors behave linearly with a range of one to six inches. Measurement for less than one inch returns as 727 and 764 counts for sensor 1 and sensor 2 respectively. Similarly, measurement more than six inches returns as 821 and 869 counts for sensor 1 and sensor 2 respectively.
Light Sensor Calibration
1000 900 Light Sensors Value 800 700 600 500 400 300 200 100 0 0 1 2 3 4 5 6 7 Distance (in)
Light Sens 1 Light Sens 2 Linear (Light Sens 1) Linear (Light Sens 2)
y = 18.2x + 765.13
y = 17.943x + 723.53
Figure 20: Light Sensor Calibration
*Refer to Appendix B for description of part load counter, velocity sensor and weight sensor
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DESIGN AND OPTIMIZATION
4.1 Conceptual
Requirement Phase
Conceptual Design
Specification Phase
Detail (Embodiment) Design
Design Phase
Implement
Integration
Integration • Trial/Error • Simulation
Operation
Figure 21: Lego Robot and Mecbot Hierarchy Diagram
4.1.1 Requirement Phase
1. The Ryerson mobile robot (Mecbot) is waiting behind the wall with bumper switches. 2. The Lego robot starts to move; climbs up and down stairs. 3. It will follow the wall using sensors. 4. Lego robot will push the bumper switch of Ryerson mobile robot (Mecbot).
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5. The Ryerson mobile robot will start move forward (using sensors) following the black strip on the floor.
4.2 Specification Phase
The specification phase shows matrices with functions required (FR) and the design parameters (DP) available for those functions. The design matrix (DM) is obtained by checking which parameters are required for a particular function. A best design would have only one parameter per function, and hence a diagonal DM. A design with all diagonal DM’s would be most efficient system. Multiplying DM with DP gives all the parameters required for a particular FR
4.2.1 Power System
FR DM Power on board - MCU (Lego) 1000 Power on board - MCU (Mecbot) 1 0 0 0 = Actuate (Lego) 1110 Actuate (Mecbot) 1101 DP Batteries / AC / DC DC Motors Touch Sensor Bumper Switch
4.2.2 Design 4.2.2.1 Mechanism
Wheels, track system, gears and frame to move (forward / backward, turn and climb up / down).
4.2.2.2 Power
Batteries and adapter to operate sensors, controllers, and actuators.
4.2.2.3 Control
Touch sensor, light sensor, and time based controls to send commands to MCU.
4.2.2.4 Sensors
Touch sensor to start, light sensor to position at a distance from the wall and to position turning, and time-based sensors to position turning.
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4.2.3 Design of Mechanism:
1. 2. 3. 4. Design the frame robust such that it is able to withstand and absorb the force exerted by the stairs when in contact. Design the frame with evenly distributed weight which prevents the robot from tipping while climbing the stairs. Design the frame such that gears and other accessories are high enough to clear the steps while climbing and do not cause any interference. Design the gear system such that it has enough torque to lift the robot over the steps.
4.2.3.1 Design of Power:
1. Choose the batteries and adapter with enough power to drive the car and is according to class requirement.
4.2.3.2 Design of Control:
1. Choose sensors and program the car such that the design requires minimum number of sensors and provides maximum functions.
4.2.3.3 Deigns of Sensors:
1. 2. Choose touch sensor. Choose light / infrared sensor.
4.3 Integration 4.3.1 Virtual Prototyping:
• • • Create a model for selected components. Design a simulation program to simulate performance. Compare results to specification and apply modifications if necessary.
4.3.2 Physical Realization:
• Acquire components and apply physical realization.
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• •
Test the system. Compare results to FRs and specifications and apply modifications if necessary.
4.3.3 Operation
• • • Test the system for N-cycles. Test the system for robustness. Compare results to specifications and apply modifications if necessary.
4.4 Mechanical 4.4.1 Mechanical System
FR DM Forward / Backward (Lego) 1001010 Forward / Backward (Mecbot) 0 1 0 0 1 0 1 Turn Left / Right (Lego) 1001010 = 0100101 Turn Left / Right (Mecbot) Climb Up / Down Stairs 1011010 Stop (Lego) 1011010 Actuate Mecbot 1001010 DP Wheels (Lego) Wheels (Mecbot) Track System (Lego) Gears (Lego) Gears (Mecbot) Frame (Lego) Frame (Mecbot)
4.4.2 Relation of Power System to Mechanical System
FR DM Wheels (Lego) 0010 Wheels (Mecbot) 0010 Track System (Lego) 0 0 1 0 = 0000 Gears (Lego) Gears (Mecbot) 0000 Frame (Lego) 0000 Frame (Mecbot) 0000 DP
Power On-board - MCU (Lego) Power On-board - MCU (Mecbot) Actuate (Lego) Actuate (Mecbot)
4.5 Control 4.5.1 Control System
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FR DM Control Motor (Lego) 100000 Control Motor (Mecbot) 010000 Interface Digital (Lego) 001000 = Interface Digital (Mecbot) 0 0 0 1 0 0 Interface Analog (Lego) 000010 Interface Analog (Mecbot) 0 0 0 0 0 1
DP Digital Output (Lego) Digital Output (Mecbot) ADC (Lego) ADC (Mecbot) Digital Input (Lego) Digital Input (Mecbot)
4.5.2 Relation of Power System to Control System
FR DM Control Motor (Lego) 0010 Control Motor (Mecbot) 0001 Interface Digital (Lego) 1000 = Interface Digital (Mecbot) 0 1 0 0 Interface Analog (Lego) 1000 Interface Analog (Mecbot) 0 1 0 0 DP Power On-board - MCU (Lego) Power On-board - MCU (Mecbot) Actuate (Lego) Actuate (Mecbot)
4.6 Sensory 4.6.1 Sensor System
FR DM Sense Contact (Lego) 100000 Sense Contact (Mecbot) 010000 Sense Wall (Lego) 001000 Sense Black Strip (Mecbot) 0 0 0 1 0 0 = Measure Distance (Lego) 001010 Measure Distance (Mecbot) 0 0 0 1 0 1 Measure Rotation (Lego) 001010 Measure Rotation (Mecbot) 0 0 0 1 0 1 DP Touch Sensor (Lego) Bumper Switch (Mecbot) Light/Infrared Sensor (Lego) Optical Edge Detector (Mecbot) Time (Lego) Time (Mecbot)
4.6.2 Relation of Power System to Sensor System
FR DM DP
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Sense Contact (Lego) Sense Contact (Mecbot)
1000 0100 Power On-board - MCU (Lego) Power On-board - MCU (Mecbot) Actuate (Lego) Actuate (Mecbot)
Sense Wall (Lego) 1000 Sense Black Strip (Mecbot) 0 1 0 0 = 1000 Measure Distance (Lego) Measure Distance (Mecbot) 0 1 0 0 Measure Rotation (Lego) Measure Rotation (Mecbot) 1000 0100
4.6.3 Relation of Mechanical System to Sensor System
FR DM Wheels (Lego) 10101010 Wheels (Mecbot) 01010101 Track System (Lego) 1 0 1 0 1 0 0 0 Gears (Lego) = 00000000 Gears (Mecbot) 00000000 Frame (Lego) 10101010 Frame (Mecbot) 01010101 DP Contact Sensor (Lego) Contact Sensor (Mecbot) Wall Sensor (Lego) Black Strip Sensor (Mecbot) Distance Sensor (Lego) Distance Sensor (Mecbot) Rotation Sensor (Lego) Rotation Sensor (Mecbot)
4.6.4 Relation of Control System to Sensor System
FR DM DP Contact Sensor (Lego) Contact Sensor (Mecbot) Wall Sensor (Lego) Black Strip Sensor (Mecbot) Distance Sensor (Lego) Distance Sensor (Mecbot) Rotation Sensor (Lego) Rotation Sensor (Mecbot)
Control Motor (Lego) 00000000 Control Motor (Mecbot) 00000000 Interface Digital (Lego) 10001010 = Interface Digital (Mecbot) 0 1 0 0 0 1 0 1 Interface Analog (Lego) 00100000 Interface Analog (Mecbot) 0 0 0 1 0 0 0 0
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5
IMPLEMENTATION ISSUES AND EXPERIMENTAL RESULTS VERSUS SIMULATION RESULTS
From the simulation (SimMechanics model) of the initial design, it appeared that the front part of the robot would climb the stairs but no conclusion could be drawn for the back portion of the design. Hence the simulation was inconclusive and an actual model was built to further examine the robot. The robot (built from initial design) did not climb the stairs and from the analysis of its run, the following problems were encountered: (1) not enough friction, (2) not enough torque, (3) stair edge clearance, and (4) center of gravity. The front wheels got up the first step but due to the lack of friction, it kept slipping at the second step. The amount of torque on both the front and back wheels was not sufficient. In particular, the back end of the robot needed a substantial increase in torque. Although the front end successfully elevated, the back end did not have enough power to move the robot forward, past the first step and onward. The chassis had motors and other pieces were mounted close to the stair height. This also prevented the robot from climbing up the stairs due the impedance of parts due to the design. Finally, the center of gravity was located closer to the back end; as a result, at times the robot would topple backwards after climbing the first step due to the imbalance of the weight distribution.
Two Wheels
Track with Belt V-Frame High Gear
Figure 22: Implementation of Improved Design Parameters
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Based on the complications of our original design, the design team decided to pursue a new design that would rectify the problems encountered. The process followed for the new design is detailed in section 4. In order to overcome the problems encountered in the initial design, extra wheels were added at the front to increase friction, design was changed to increase torque by changing our gear train in both front and rear drive, V-frame was introduced to avoid interference with the stairs, and weight was distributed more evenly throughout the robot to prevent it from tipping (refer to Figure 22)
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6 DISCUSSION AND CONCLUSION
The most important part of the course was the stair climb and our robot climbed the stairs consistently without a hitch. It also followed the wall consistently at the end of the stairs. The Mecbot followed the black strip every time once actuated as well. The only drawback in the design was the final left turn, which wasn’t perfect and often missed the bumper switch on the Mecbot. There are no perfect designs and all designs need improvements. In this design, there are several things that could be changed to make the design more efficient. Firstly, the turning took long time compare to travel time and also some of the wheels were dragging. If the robot was all wheel drive with one motor controlling right wheels and another motor controlling left wheels; the turning could have been more efficient as all wheels would be in motion resulting in less drifting. Secondly, the robot fairly long and this required wide turns and also turning took longer. If the robot were more compact, turning would be more accurate, faster, and would also eliminate wide turns. A technical problems encountered during the project were inconsistency in sensor reading. The reading varied every time under same environmental conditions (i.e. lights off). The reason for being the sensor was too old and was wearing down. Overall the project was a success as all assigned tasks were completed. There was a lot learned from this project and it helped enhance our technological knowledge and further develop our problem solving skills. In future projects in industry, we would definitely apply the skills acquired in this course. We understand that a thorough design analysis and simulation prior to building a model or prototype is vital in a project as it saves time and money.
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7
REFERENCES
[1] Brear, David, comp. "Lego Dacta Robotics and Helpful Web Sites." 5 Mar. 2008
. [2] "Lego Mindstorm & Technic (Spare Parts and Accessories)." 2 Mar. 2008 . [3] "Track 2 Remote Operation Challenges." BotBrain Educational Robots. 22 Mar. 2008 . [4] Necsulescu, Dan. Mechatronics. New Jersey: Prentice Hall, 2002. [5] Bagnall, Brian. Lego Mindstorms Programming. New Jersey: Prentice Hall, 2002. [6] Hystad, Dean. Building Lego Robots for First Lego League. Minnesota First Lego League. Innovations in Science and Technology Education, 2002. 03 Mar. 2008 . [7] Sharifi, Farrokh Janabi, “MEC 830 Mechatronics Design”, Ryerson University, 2008, 06 April. 2008
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APPENDIX A - ANALYSIS OF STALL TORQUE
Theoretical Calculations
Stall Load Motor1: 230 g Motor2: 240 g Armature Radius: 20 mm
Sample Calculation --Calculating Kt ωn = u/Kt Kt=9/32.5=0.277 Nm/A --Calculating Ts (stall torque) Ts = (Stall Mass)(Acceleration due to Gravity)(Armature Radius) Ts =(0.225kg)(9.81m/s2)(0.020m)=0.044 Nm --Calculating R Ts = uKt/R R = uKt/ Ts R = (9V)(0.277Nm/A)/(0.044Nm)=56.7 Ω --Calculating Max Power Mechanical Power: Tmax=0.5 Ts = 0.022 Pmax = ωnTs/4=(32.5rad/s)(0.044Nm)/4=0.358 W Electrical Power P=ui=(9V)(0.1A)=0.90 W
A-1
Torque Vs. Speed
0.045 0.04 0.035 Torque (Nm) 0.03 0.025 0.02 0.015 0.01 0.005 0 0 5 10 15 20 25 30 35 Speed (rad/s)
Figure A 1: Torque vs Speed for Motor 1
Torque Vs. Speed
0.06 0.05 0.04 0.03 0.02 0.01 0 0 5 10 15 20 25 30 35 Speed (rad/s)
Torque (Nm)
Figure A 2: Torque vs Speed for Motor 2
A-2
Max Power Motor 1
1 0.9 0.8 0.7 Power (W) 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 Speed (rad/s) Mechanical Electrical
Figure A 3: Max Power Motor 1
Max Power Motor 2
1 0.9 0.8 0.7 Power (W) 0.6 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 Speed (rad/s) Mechanical Electrical
Figure A 4: Max Power Motor 2
A-3
Practical Calculations
A-4
From the experiment it is clear that stall torque for both motor 1 and 2 are 0.03946 Nm and 0.03889 Nm respectively. In comparison to theoretical values, there is now friction involved with the car and the static load; as a result, the motor has to overcome this additional resistance. For theoretical calculation, the motor was stationary, and was attached to a pulley system, in this case, the motor was constructed to be part of the system where it was mounted on the car, and utilized with gears and wheels. As a result of the motor being mounted with the car, there was also additional resistance on the motor that it had to overcome from the friction between the gears. Previously, these additional resistances did not exist, and the existing frictional sources were small enough to be considered negligible; therefore, the practical stall torques values were less because it was combined with the additional resistances.
A-5
APPENDIX B – PART LOAD COUNTER, VELOCITY SENSOR & WEIGHT SENSOR
B.1 Part Load Counter
Design a PART LOAD COUNTER using a touch switch from the Lego Mindstorm kit, write an IC program for the counter and display the counts on the screen.
int part_no, i, touch; void main() { part_no =0; while(1) { if (touch(1)==1) /*touch sensor attached to channel 1 is hit */ { sleep(0.50); /* gives time to take back the finger */ part_no = part_no +1; /* accumulates the part # */ } printf("%d\n", part_no); /* displays the number of parts */ } }
B.2 Velocity Sensor
long sensor_time[2], Vel, Speed; int i; void main() { reset_system_time(); //could be alternatively reset by pressing reset switch. i=0; while (i < 1) { if (irproxright()>110) { beep(); sensor_time[i] = mseconds(); //returns the count of system time in msec printf("%d \n", i); i++;}} i=1; while (i < 2) { if (irproxleft()>110)
B-1
{ beep(); sensor_time[i] = mseconds(); //returns the count of system time in msec i++;}} Speed = ((4.85/(sensor_time[1]-sensor_time[0])); printf("%d \n",Speed); } /*distance between sensors=4.85inches trial 1=320 ms trial 2=324 ms trial 3=323 ms*/
The lego car goes past the 2 infrared sensors of the MCU robot which would beep when it detects the lego robot each time and would record the number of the beep, whether it is the first reading or the second, and then display the speed of the lego robot on its LCD screen. The distance between the 2 infrared sensors on the MCU robot was known, therefore by dividing that distance by the time the lego robot takes to travel between the infrared sensors, it is possible to calculate the speed of the lego robot.
B.3 Weight Sensor
int sensor_reading; long Weight; void main() { while (1) { irproxleft() == sensor_reading; Weight ==((-1.4887*sensor_reading)+311.14); printf("Weight is %d\n", Weight); } } The system is designed to attach a few known weights to a string over a pulley and the other end of the string attached to a sliding face with a rubber band and the other end of the rubber band fixed. In order for the readings to be “successful” the Lego parts had to be fixed along with the rubber band so that the length of rubber actually undergoing deformation was consistent. The infrared sensor also had to be fixed so that our reference point is consistent. By calibrating the readings from the infrared in relation the applied mass, the weight sensor is created.
B-2
Figure B 1: Load Sensor Mechanism
Weight (g) 90 105 112 120 134
IR reading 162 158 145 132 121
Table B 1: Experimental Observations
B-3
IR reading Vs Load
y = -1.4887x + 311.14 200 180 160 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 140
IR reading
Load (g)
Table B 2: Linear Relationship between IR Reading and Load
B-4
APPENDIX C – C Programming
RCX Mindstorms Flowchart
C-1
RCX Mindstorms Program
int i=0; int j=0; int k=0; int Number_turns = 2; void main () { while(1) { while (j<1) { forward(); if (touch(1) == 1) { right_turn(); i=1; } if (i==1 && light(3) > 854) { left_turn(); i=2; forward(); sleep(1.0); } if (i==2 && light(3) > 864) { left_turn2(); i=3; } } if (i==3 && touch(1)==1) { ao(); } } } void forward() { fd(1); fd(2); fd(3); }
C-2
void left_turn() { while (light(2) > 800) { motor(1,48); motor(3,-80); motor(2,80); } } void right_turn() { while (light(3) > 740) { motor(3,100); motor(2,-100); motor(1,0); ao(); } } void left_turn2() { while (light(2) > 800) { motor(1,48); motor(3,-100); motor(2,100); }}
C-3
Mecbot Program
int LEFT_MOTOR = 1, RIGHT_MOTOR = 0, BMP, wall; int LEFT_EDGE = 50, RIGHT_EDGE = 50; int speedr, speedl; persistent int goal; void main() { ao(); while(1) { BMP = 0x0f & peek(0x1500); printf("StartMe -> %b \n", BMP); if (BMP==0x0e || BMP==0x0d || BMP==0x0b || BMP==0x07 || BMP==0x09) { //sleep (1.0); speedr= 50; speedl= 50; while (1) { if (edgeright() >=RIGHT_EDGE && edgeleft() >=LEFT_EDGE) { forward(speedr, speedl); printf("Forward %d\n", edgeright()); } if ((edgeright() = LEFT_EDGE)) { backward(60,60); sleep(0.1); right(50); printf("Right\n"); } if ((edgeleft() = RIGHT_EDGE)) { backward(60,60); sleep(0.1); left(50); printf("Left\n"); } if ((edgeleft()