Playing With Gears

This chapter in the LEGO robotics book overviews the importance of using gears to improve the functionality of your robot and to ensure proper usage of gears.
First off, the main theory behind a gear is that by using a gear to turn another gear of a different size, you can either multiply the force behind that second gear, or greatly accelerate the speed at which that gear travels. In the above example, the gear being used to turn the other gear is known as the driving gear, and the gear being turned is known as the driven gear. The forces being outlined in the above example are essentially torque, and what is known as angular velocity, or 'speed'. Torque is a product of force and distance and basically is the amount of kick or driving power behind a gear. Angular velocity is the rate at which your robot will cover distances.
When wanting to increase torque on a robot, the driving gear would have to be smaller (have fewer teeth, ie. little pegs) than the driven gear and vice versa for the driven gear. So based upon this concept one would think that you should just add as many gears as possible to magnify your robots capabilities. However, this is where another catch is met: a force called friction. Friction is the amount of force being transferred between the teeth of your gears; and consquently, having more gears means more teeth and thus more friction. Having too much friction can damage the robot, gears, and whatever motors are driving it; thus a proper balance must be found.

There are also many types of gears that can be used for several different situations. For example, a gear known as a knob wheel (four rounded teeth) is a gear that is specialized in providing more torque as its larger surface area on the teeth allows more energy to be transferred. Another type of gear, known as a clutch gear is essentially a 'safety' gear that locks down when too much force is applied to it. This gear is useful in protecting the rest of your gears and robot in case too much force is exerted.

In addition to just connecting gears to gears; gears can be connected using pulleys and chains. Using pulleys and chains allows you to connect gears that would normally be too far away to just stick in a bunch of other gears to connect. Pulleys also have the advantage of being much quieter than gear connections. The difference between pulleys and chains lies in the forces they are better suited to dealing with. Pulleys, using belts tend to have very little grip on the gears and as a result produce very little torque, which is good if you are going to for angular velocity. Chains however are composed of individual links and have the most amount of grip on the cogs on the gears. This means that they produce the most torque and are relatively poor for use when trying to achieve high angular velocity.

Getting in Gear Investigation

Today we started to work with gears and experimenting with gear ratios.

We experimented with making both the driven and driving gears larger. We did this be switching which gear (24t/8t) was attached to the motor. The driving gear is the gear attached to the axle attached directly to the motor, the driven gear is the gear that is attached to the axle attached to the wheel (turned by driving gear). We found that making the driving gear larger than the driven gear speeds up the robot based on the ratio of the teeth on the wheels. However by making the driving gear smaller than the driven gear means that the gear has to rotate multiple times to turn the other gear once. This slows down the robot however adds considerable torque to the robot (torque is basically the power/driving strength behind a motor) .

The highest speed we would be able to achieve with the taskbot NXT model without using gear trains would be with using a gear ratio of 40t to 8t with 8cm diameter wheels.

However, as we came to realize, having a setup with high gear ratios and high angular velocity creates a potentially hazardous situation for the NXT motor and gears. If for whatever reason the robot hits an obstacle and doesn't stop, then the motors multiplied driving force of the gears can bend or mangle parts of the NXT. Having some sort of PANIC! button here would be useful...or perhaps just adding a touch sensor to the front of the robot underneath some sort of ramming shield.

Classic Projects

This chapter basically summarizes two projects that are often undertaken and are an ample introduction into the fun yet complex world of programming and constructing effective robots.
The first project concerns the navigation of your room. The robot to be constructed for this project will require at least one touch sensor and ultrasonic sensor to be successful in this task. A robot optimized for this task however would probably incorporate the use of at least two touch sensors, the ultrasonic sensor as well as a bumper design and special gearing. The bumper would probably be split into two sections as it allows for more coverage and allow the robot to turn based upon which touch sensor was hit, in relation to which bumper was pressed. The only limitations with this kind of bumper however are that it increases the likelihood of the robot being too wide and getting stuck on awkward inward facing angles such as where walls meet. The gearing (1:3, meaning that for every rotation of the motor, the wheel would turn a third of its normal capacity) would be used to slow down the robot so that a more cautious approach could be used to explore your room in case the robot falls into dangerous pitfalls that would be harmful to the robot (stairs...). These additions are what differentiate a robot that is optimized for a project, and those that simply 'work.'

The second project involves line tracking and covers several methods to both increasing tracking speed, accuracy and design more efficient robots. When line tracking the important to remember is the amount of hysteresis your robot creates. Hysteresis is the amount of 'sway' the robot has as it travels over the line; more sway means less control and less speed in this case. It is also suggested to place the light sensor 5mm-10mm to the ground to maximize the amount of reflected light and reduce the chance of the robot veering off of the line (If it has too much speed).

The Course Robot

The key points from chapter six to remember when building are:

• Modularity
• Balance - low center of gravity = stability
  
• lightweight and strong as possible
• Proper structural support

Of these points, as my partner and I are planning to create a robot that is both slim, low to the ground and light-weight; we will use the concepts of balance, lightweight structural support and keeping the robot low to the ground. These will keep the robot from flipping over during the various obstacle course challenges as well as reduce unneeded weight which could slow down the robot. More to come...

...Today we worked on programming the robot to make the first leg of the course. This included setting up a light sensor and touch sensor as well as getting the robot to run straight. For the most part the program was successful, however the robot had difficulties in keeping a straight path. For the challenge this will be our main concern.

For Monday we will have to setup the program for the ultrasonic sensor as well as create the evasion program for our ultrasonic sensor on the last leg of the course.

After COUNTLESS on-course tests and the never ending re-balancing of the our course-bot...and admittedly due to calculating the angles at which the robot generally steered off of course...Hakyoon and I finally managed to navigate the obstacle course, scoring perfect 10's across the course with the exception of the last leg where the robot skimmed the can and earned us a lowly 7 :S

Building Strategies

(NOTE: This entry is a work in progress)

Chapter six of the Lego Robotics book emphasizes the importance of the structure of your Lego Robot. When creating a robot, the main goals you want to keep in mind, are that you want to keep the robot as lightweight as possible - using minimal amounts of bricks - without sacrificing the structural integrity of your robot and making it very vulnerable to forces such as compression and tension (unless you have alternative intentions for your robot). Compression is a force exerted on structures that pushes and tries to make the structure smaller, while Tension is the opposite; it stretches and tries to elongate the structure. To counter both forces and to make your robot more 'economical' by using less parts for more strength, a variety of different supports must be used in combination (ex: beams and 'L-beams' must be used together).

When it comes to structural integrity, protecting the gears and motors of your robot are vital, as in relation to the human body, they are the heart of your robot; driving it forwards and turning it into the unstoppable monster, or lithe dragster that it is. The important thing to remember with gear and wheel placement is that the closer the gear/wheel is to its supporting beam the better. Having the gear/wheel closer to its supporting beam means that less force (generated by the mass of the robot for example) will be pushing down on the axles and pushing your gears apart. Another point to remember when supporting gears is to mount supports in line with the gears, as illustrated in 6.10, 6.11 of the robotics book. This means that if your gears are operating horizontally - match parallel support beams horizontally. Having the axles snap under multiplied pressure, or your gears failing to function as they slide apart are realities that can be easily solved by remembering these points.

Also, when constructing a robot it is also important to remember to balance the robots weight between both the driving wheels and any other wheels on the robot (generally slightly more weight on driving wheels) so the robot isn't off balance.

Finally, another important thing to remember is to build your robot with modularity. This means that you should construct portions of the robot together so that you can easily attach and detach certain portions of the robot to easily remake the structure. When building a robot using both the Technic and Mindstorms kits, also known as a hybrid, modularity is one advantage the robot has compared a purley Mindstorms kit in most cases (Hybrid robots also tend to be heavier and more stable) .

Challenge: Obstacle Course

My Lego Robotics team (yet to be decided) has been presented with the challenge of building a robot that will be able to navigate an obstacle course with several kinds of obstacles; in this challenge our robot will have to use most of the sensors we have been taught to use so far.
The robot must first travel forwards and stop within a boxed out region for five seconds, a light sensor will be used here, after this the robot must ram in to a wall and activate a touch sensor before reversing and turning right. After this the robot will travel forwards and use its ultrasonic sensor to detect a wall, and turn right again. The final leg of the course calls for the robot navigating a randomly placed obstacle; this would probably be done with the use of a ultrasonic sensor and if time allows, some sort of lego 'missile' that will remove the obstacle from the course.

(All of the above while smoking the competitors' robots navigation times of course)

Essentially I am only brainstorming as to the actual design of the robot at the moment...and I'm clueless...so far:

• The robot should be low to the ground - probably longer than taller for balance and aerodynamics :O
• Will need multiple appendage like structures to hold variety of sensors in place and to prevent overlapping of sensors
• May use gear trains to juice all of the possible speed out of the robot (losing torque shouldn't be an issue as it is a flat course)
• The largest Lego wheels possible should be used for additional speed.
• The touch sensor will have to be mounted on the front, as well as the ultrasonic sensor, so some variations in height will be necessary.
  

Understanding Lego Geometry

Essentially this chapter gets at the bare bones, or bricks in this case, behind Lego construction. In the world of Legos, measurements and sizes of bricks are noted by the number of studs on a Lego brick, also known as Lego units. When stating the sizes of Lego bricks, it is stated in dimensions in the order of, width, length and finally height. Width is determined as being the shorter of the two horizontal sides of a Lego brick when it is laying 'studs up.' For example, the smallest Lego brick has dimensions of 1 x 1 x 1 Lego units, however this does not mean that it is a cubular shaped brick. In the world of Legos, one 'stud' has a ratio of 6:5 when comparing height to width in milimeters, thus explaining why the one stud Lego 'cube' isn't really a cube.

When comparing Lego bricks to Lego plates, Lego plates are approximately 1/3 the height of one stud.

However, bricks and plates are for those of you that like to kick it Oldskool, as the NXT Mindstorms sets use the newer Lego Technic pieces. The Technic pieces are essentially studless versions of the Oldskool blocks that are more weight efficient and less cumbersome when it comes to precise and lightweight building, that retain the same strength.
With the studless beams and liftarms in the Technic set, capabilities such as diagonal crossbracing become a possibility. When diagonally crossbracing with studless beams, one can use Pythagorean's Theorem to calculate if a certain beam can be used to crossbrace a structure.
Pythagorean Theorem essentially is a formula that relates the measurements of the hypotenuse of a right angle to being equal to the squared values of the other arms...
In other words...a^2 + b^2 = c^2, where c is the hypotenuse.
For example a structure with a base of 15 units, and a height of 8 units can be crossbraced because:
15^2 + 8^2 = 17^2, c in this case equals to a number whose square is a whole number, meaning a studless beam could be used to crossbrace.

I apologize as this is a rather long-winded post...however to conclude my summary of the chapter, one can also use liftarms to brace Lego structures. The key difference here is that liftarms arent straight beams, meaning that one can use them regardless of the Pythagorean Theorem to brace a structure from impacts in totally unique ways.

Field of View Experiment

In order to test the capabilities of the the NXT ultrasonic sensor we conducted an experiment to demonstrate the width and length ranges at which the NXT sensor was still functional.

1. We layed our NXT robot, equipped with an ultrasonic sensor on the front of the robot, on a flat white board. The program detecting distance (cm) under 'view' was run.
2. After this, white masking tape was layed directly in front of the robot in a straight line for 2 meters.
3. Intervals of 10 cm were marked on the white tape
4. An object (Whiteboard eraser, flat side towards sensor) was slid down the white tape until the ultrasonic sensor no longer detected it. This position was marked with black tape.
5. At every 10 cm interval the whiteboard eraser was slid left and right until the sensor no longer detected an object. These positions were also marked with black tape.

Once the procedure was finished we marked down the black tape points on a smaller a4 paper which was divided into a grid. The distances were scaled down so as to fit onto the a4 grid, personally I used a scale of 2:1.

Now looking at the black tape pattern our group recognized that when an object was closer to the sensor, the sensors field of view was narrow (~5cm either direction). However past a certain distance, (~40-70cm) the sensors field of view widened to a maximum of about 20cm before gradually shrinking down in width to the maximum distance the sensor could read.
This formed a somewhat balloon-like shape.

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