Unit 7

Mechanisms

The primary focus of the Robot Gladiator League experience is to design, build, battle test, and refine robots that do specific tasks or sets of tasks you want them to do. This could be to score points, defend your end zone, or smash your opponents’ robots. Regardless of the role you want your robot to play during the melee competitions, chances are that you are going to build some sort of mechanical structure or mechanism as part of your robot.

A mechanism is a system of rigid parts connected together and working within a machine to perform a specific function. The function they perform is usually a desired motion or the application of a force on another part of the machine to which they belong or to an outside object. Mechanisms come in all sizes and shapes, are made of many different materials, and perform all sorts of functions. Mechanisms can consist of a few simple parts or be highly complex. Most likely, some of the mechanisms you build in RGL will be designed to apply forces on outside objects that are not part of your robot, that is, to your opponents’ robots. However, certain mechanisms on your robot will have the function of making other parts of your robot move or function, and you need to know how to create those part to build a competitive machine.

There are four different types of weapon mechanisms you can incorporate into your robot design:

1. Spinners
2. Flippers
3. Hammers
4. Spears and rams

Each one of these consists of simpler mechanisms and you will need to understand how those mechanisms work together to create a successful, functioning weapon.

Simple Machines

Many mechanisms, including the ones listed above, consist of one or more simple machines which are the oldest machines known to humans. There are six types of simple machines and you may include one or more of them in your designs:

1. Levers
2. Inclined planes
3. Wedges
4. Pulley
5. Wheel and axle
6. Screw

Simple machines are used to multiply or change the direction of force, making it easier to perform work. The amount by which simple machines theoretically multiple force is called their ideal mechanical advantage, or simply IMA. This is always greater than the reality of the realized force increases because machines have friction, thus reducing the force multiple. In general, mechanical advantage, or MA, is the true ratio of force output by a machine versus the force input. It should be noted that MA is always less than IMA in real situations.

Each machine has a different technique for determining ideal mechanical advantage. Let’s look at each type of simple machine individually, then we will relate them to the 4 types of weapon mechanisms listed earlier.

Levers

A lever is a rigid bar that pivots about a pivoting point, called a fulcrum. There are 3 classes of levers:

Levers can be used to lift heavy weights or to exert high forces on objects. The lever’s ideal mechanical advantage is given by the following equation:

Where the “input arm length” is the distance from the effort force to the fulcrum and the “output arm length” is the distance from the fulcrum to the resistance force exerted by the machine.

Inclined Planes

An inclined plane is a slanted surface over which loads are moved to make them easier to move.

Most inclined planes are stationary and the object is pushed or pulled up the plane. Many inclined planes are used to load cargo into trucks. The inclined plane’s ideal mechanical advantage is given by the following equation:

Where the “length of incline” is the actual length of the hypotenuse of the triangle the inclined plane makes and the “height of incline” is the vertical distance (y-axis) from the bottom of the ramp to the top.

Wedge

Wedges are similar to inclined planes except they can be thought of as two inclined planes placed back-to-back. Wedges typically perform the task of splitting or dividing things.

The wedge’s ideal mechanical advantage is given by the following equation:

Where the “length of one side” is the actual length of one of the longer sides of the wedge and the “width of the wedge” is the horizontal distance (x-axis) separating the two long sides opposite of the point.

Pulleys

A pulley consists of a disc on an axle that redirects the force exerted by a rope or flexible cord. Multiple pulleys can be used, as below, to multiply the effort force so that heavier loads can be lifted. Therefore, pulleys can change the direction of a force and can be used to amplify forces.

The ideal mechanical advantage of a pulley system depends on the arrangement, or type of pulley system being utilized.

• For single fixed pulleys, the IMA=1; in other words, you must exert an effort force equal in magnitude to the load being lifted.
• For single moveable pulleys, the IMA=2. In this case, the pulley will lift a load twice as heavy as the magnitude of the effort force.
• For Gun Tackle systems, or multiple pulleys, the ideal mechanical advantage is given by the number of rope segments supporting the load. Here, we must make sure we do not count the rope segment where the effort force is applied. In the diagram above, the IMA of the Gun Tackle system is IMA=2.

There are several different configurations of pulley systems and each one has its own application. The ones above changed direction of force and in some cases multiplied force. An example of one type of pulley system designed to transmit rotational motion from one shaft or axle to another is seen below. Assuming the pulleys are of equal radius, there is no multiplication of force.

Wheel and Axle

The wheel and axle machine is probably the most influential simple machine in all of human history. It allows us to more easily move things from place to place. Wheel and axle machines are found almost everywhere. This simple machine consists of a round disc that is either rigidly attached to or rotates on an axle. Typically, the wheel has a larger radius (R) and the axles has a smaller radius (r).

The wheel and axle’s mechanical advantage is given by the following equation:

Screw

A screw is an inclined plane wrapped around a shaft. Screws convert rotational motion to linear motion and this linear motion can exert great force. Screw jacks are a mechanism that take advantage of this fact.

The screw’s mechanical advantage is given by the following equation:

Where the “circumference of screw head” is and the “thread pitch” is the distance between two threads.

Weapon Mechanisms

So, how do all these simple machines relate to our Robot Gladiator League weapons? All four weapon styles are themselves simple machines or they incorporate multiple simple machines to function. Let’s take a look at each weapon style.

Spinners

Spinners are rotating bars or blades that are powered by an electrical motor. Spinners use a wheel and axle as well as a pulley system to operate. Later, we will discuss in greater detail how the pulley system makes a spinner work. Spinners can rotate at frighteningly high rpms (revolutions per second) and can cause tremendous damage. These weapon systems are generally offensive in nature.

To build a spinner, you must construct or utilize at least three mechanisms: a motor mount, a clutch, and an axle mount. Pictures of each are shown below. The shaft in the axle mount holds your actual spinner blade.

Axle Mount

Clutch

Motor Mount

You will also incorporate two pulley systems amongst all three of these mechanisms.

Flippers

Flippers utilize an inclined plane coupled with a lever system and a pneumatic system to lift or overturn other robots. Notice the top right corner of the robot has a sloping bar that is the end of the inclined plane. Notice also that two pneumatic actuator cylinders are needed to power this flipper.

To build a flipper, you will need to build your inclined plane, a lever framework that supports and rotates your flipper surface, and mounts to attach your pneumatic cylinders to the robot chassis.

Cylinder Mount

Hammers

Hammers are pneumatically powered weapons that can swing horizontally or vertically. The one shown below is a vertically acting hammer. They are simpler to build than spinners and flippers and can produce considerable damage to other robots.

Hammers require a hammer pivot mount and two cylinder mounts, one on the hammer and one on the robot. The placement of these mounts relative to each other greatly affects the range of motion of the hammer, and you will have to experiment with their placement to get the range of motion you want.

Rear Cylinder Mount

Forward Cylinder Mount

Hammer Mount

Spears and Rams

Spears and rams are the simplest of the weapons to build. They are essentially wedges on the ends of beams that poke other robots. They do not require additional power to operate, they are rugged and less prone to damage, and do considerable damage when used by a skilled driver. Note the wedge shape on the end of the spear.

To build a spear or ram, a shaft is bolted directly to the robot top plate. The primary means of using a spear or ram is by driving the robot into your opponent, spear first. A skilled driver can keep another robot at bay with his or her spear, as well as break parts of other robots.

More About Pulleys

Pulleys are one of the simple machines, and there are 2 pulley systems on your robot platform, one for each drive wheel. If you choose to make a spinner weapon, you will have to build two more pulley systems to make it spin. You can also change the maximum speed of your robot by understanding how pulleys work. This section presents how to use pulleys and how to calculate the output speed given an input speed.

As described in the mechanisms section, pulleys are a type of simple machine consisting of a circular disc that rotates about an axis. The pulley system used in RGL is actually a timing pulley system. Timing pulleys are pulley wheels with little grooves, or teeth, cut into the faces of the wheel to allow the belt to grip it and not slip. They are somewhat of a cross between a smooth pulley and a gear. Notice that the timing belt has teeth that interface with the timing pulley wheel.

Some Terminology:

1. Drive Pulley – the wheel that is attached to the power source, usually an electric motor.
2. Driven Pulley – the wheel that is turned by the belt and the driving wheel.
3. Center to Center Distance – the distance between the center of the two axles on which the pulley wheels rotate.
4. Pitch – the distance between the teeth on the belt or the grooves in the pulley wheel.

Pulleys can be used to make a change in the rotational speed between the input shaft and the output shaft. This is all based on the size of the pulley wheels.

In the drawing above, the pulley wheel diameters are the same. The rotational speed of the driven pulley is the same as rotational speed of the drive pulley. Intuitively, this makes sense. For every rotation of the drive wheel, there is one rotation of the driven wheel. However, what happens when the pulleys are not the same size?

In this case, the two wheels do not turn at the same speed. Why is this? To visualize why this is the case, imagine a small red dot on the belt. As the belt moves, so does the dot, traveling around the wheels and moving back and forth between the wheels. Now, consider the point at which the dot just starts to go around the wheel. Both wheels are turning clockwise.

Dot starts around the wheel here.

The dot travels around the wheel moving a distance roughly half the circumference of the wheel while it is in contact with the wheel.

Dot leaves the wheel here.

Now suppose there are two dots on the belt that are spaced such that they both make contact with a wheel at the same time.

Dot 1 starts around its wheel.

Dot 2 starts around its wheel.

Both dots start around their respective wheels at the same time. Since they are both attached to the belt, they both move the same distance in the same time period.

Dot 2 travels about this far around its wheel when dot 1 leaves its wheel.

Dot 1 leaves its wheel.

Since they both travel the same distance, and since the bigger wheel has a much larger circumference than the little wheel, dot 2 does not go proportionally nearly as far around its wheel as dot 1 goes around its wheel. Dot 1 goes halfway around its wheel, but dot 2 only goes part way around its wheel.

Technically, the dots are not going around the wheels, as the wheels are rotating with the spots on the belt. However, the illustration here shows that for every half turn of the little wheel makes (It makes about half a turn while the dot is in contact with it.), the bigger wheel makes less than half a turn. This means that then big wheel is rotating more slowly than the little wheel. Whenever a little wheel drives a big wheel, the big wheel turns more slowly than the little wheel. When a big wheel drives a little wheel, the little wheel turns faster than the big wheel.

So, now the question becomes, if we have a pulley system with differing sized wheels, and we know the rotational speed of the driving wheel, how do we calculate the rotational speed of the driven wheel?

To do this, we use the following relationship:

RPM1 x Diameter1 = RPM2 x Diameter2

Where 1 indicates the driving wheel and 2 indicates the driven wheel.

We can rearrange this equation to look like this:

Equation 1

So, all we have to know is the diameters of each pulley timing wheel. There is an interesting trick, however, that makes this equation simpler. It turns out that all we really need to do is count the teeth on each wheel, and use these numbers instead of the diameters:

Equation 2

Example:

An electric motor with a 12-tooth timing pulley is driving a 36-tooth timing pulley. The motor turns at 3000 rpm. At what rpm is the driven pulley rotating?

Let’s use equation to solve this.

Solving this,

So, the big wheel turns 1/3 as fast as the little wheel.