RPM, or revolutions per minute, is a measure of the rotational speed of an object. It is defined as the number of complete revolutions an object makes around its axis of rotation in one minute. RPM is often used to describe the speed of mechanical systems, such as motors, gears, and shafts.
The relationship between RPM, torque, and the speed of a shaft is complex and depends on several factors, including the size and shape of the shaft, the type and amount of load being applied, and the efficiency of the system.
In general, the torque required to rotate a shaft increases with the speed of the shaft. This is because the faster an object rotates, the more force is required to overcome the centrifugal forces acting on it. As a result, shafts operating at high speeds typically require higher torque to maintain their rotational motion.
Conversely, the speed of a shaft is directly proportional to the torque applied to it, assuming the load and efficiency of the system remain constant. This means that increasing the torque applied to a shaft will result in an increase in its speed, and decreasing the torque will result in a decrease in its speed.
The RPM and torque of a shaft are important factors to consider in the design and operation of mechanical systems. Engineers must carefully balance these variables to ensure that the system operates efficiently and safely and that the shaft is able to withstand the forces acting on it.
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Gear ratios are one of the most common design decisions that a team must master in order to optimize mechanical advantage in their designs.
A Gear Ratio is defined as the ratio of the rotational speeds of the first and final gears in a train of gears or of any two meshing gears. Essentially, the ratio of the input speed to the output speed of a geared set of shafts. These can be decided to choose a ratio of Speed (large gear driving small gear) or Torque (small gear driving large gear).
Gear ratios are often simplified fractions of the number of teeth on each gear. This is because (at least in Vex) gears have a proportional number of teeth to their diameter which defines the difference in output speed. From the above image, there is a 12 tooth gear, driving a 36 tooth gear which would constitute a 3:1 ratio.
The benefit of gear ratios is the ability to choose speed vs torque in a system. These have an inverse relationship however where a faster output will have lower torque. With the above example, the output shaft has 3x the torque, but also 1/3 the speed.
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Torque, also known as moment of force, is a measure of the rotational force applied to an object. It is defined as the product of the force applied to an object and the distance from the object's axis of rotation to the point where the force is applied. Torque is a vector quantity, meaning it has both magnitude and direction.
Torque is often represented by the symbol "Ï„" (tau) and is calculated by the following equation
where:
τ (tau) is the torque, measured in newton meters (N·m)
F is the force applied to the object, measured in newtons (N)
d is the distance from the axis of rotation to the point where the force is applied, measured in meters (m)
Torque is an important concept in mechanics, as it is used to measure the ability of an object to rotate around an axis. It is a fundamental principle in the operation of machines, such as motors, gears, and levers, which use torque to transmit power and motion.
In robotics, the most common way that torque is important is anything relating to motors. In a drive train, torque is needed to accelerate quickly, hold a top speed, and be able to push opponents on the field. In a lift, more torque allows the ability to lift heavier loads, lift items faster, and maintain speeds during lifting. For a flywheel, torque allows for higher speed, less loss of speed between shots, and easier tuning of speeds.
In summary, torque is a measure of rotational force that is essential in the design and operation of machines and structures. It is used to calculate the ability of an object to rotate, transmit power, and withstand external forces.
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In materials science, stress refers to the internal forces that exist within a material as a result of external loads or forces acting on it. Stress in metals can be caused by a variety of factors, including temperature changes, mechanical loads, and corrosion.
There are five types of stress that can occur in metals: shear stress, bending stress, torsion stress, tensile stress, and compressive stress. In Vex robotics, the most common types are Bending, Torsion, and Compression/Tension (opposites).
The strength of a metal is determined by its ability to withstand stress without failing. When a metal is subjected to stress, it will either deform elastically (temporarily) or plastically (permanently). If the stress is high enough, the metal will eventually break, which is known as yielding or failure.
Stress can also affect the physical and mechanical properties of metals, such as their ductility, malleability, and toughness. For example, a metal that is subjected to high tensile stress may become more brittle and less able to withstand further stress.
Managing stress in metals is important in order to ensure their structural integrity and prevent failure. This can be done through various methods, such as using stress-relieving techniques, applying appropriate protective coatings, and designing structures to distribute stress evenly. In Vex, stress can be managed by assuring that loads are properly distributed and pieces are properly braced.
Bending is the most common type of stress in the robotics design process. Bending comes from a force being applied perpendicular to the length of an object. Commonly, a piece of metal that is used in a lift will have forces that cause bending.
Torsion is very common in underdeveloped robots. Torsion is caused by force applied tangent to an object's axis, commonly called twisting. Oftentimes, this is seen along long pieces of metal that might be sparsely supported or an axle in high torque situations with little support.
These two are opposite forces where a force is being applied through an axis of an object either pushing (compression) or pulling (tension). In robotics, this is often times seen at connections between pieces through screws, standoffs, or spacers that become inconsistent over time.
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Learn about all of the different engineering and design principles that go into a robot.
The center of mass (COM) or center of gravity (COG) of a robot is the mean location of all the mass of a robot.
Model the robot in CAD, and use a "measure"-type tool.]
Lift the robot by the chassis using 2 fingers. When the robot balances on your fingers, the XY location of the COM will lie in the line formed by your 2 fingers.
the robot, and observe how the robot tilts to settle.
When a robot brakes, the friction between the wheels and the floor rapidly decelerates the robot (velocity is in the opposite direction of acceleration in this case). This creates a torque around the center of mass of the robot, jerking the back of the robot up. In many cases, the rear wheels lose grip with floor as well.
To mitigate jerking ...
lower the height of the COM off the ground
use lighter materials in the upper sections of the robot (ex. 1x1 L channels on arms, plastic screws / nuts)
use heavier materials in the lower sections of the robot
decrease the max acceleration available to the driver
The of the robot is less predictable if the COM (in the horizontal plane) is far from the midpoint of all the wheels. Keeping the COM centered side-to-side and front-to-back ensures more stable and predictable turning.
The end effector used during a hang is typically implemented with a joint. If the horizontal COM is offset from the point where the robot hangs, the robot will tilt until the COM aligns directly beneath the hanging point.
To control the position of the COM in the XY plane ...
place towers optimally after building the chassis
add/remove weight selectively around the robot
implement motion profiling and other motor control techniques
