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General Physics By Nick Brennan, Sam Mills, and Matt Dunster FRC 11 - Mount Olive Robotics Team Objectives • • • • • Review for most; Introduction for some Earn a greater understanding of applicable physics concepts Recognize these concepts are used all through robot design Learn to apply relevant physics topics to FRC Have fun Physics Topics • • • • • • • • • • • • Trigonometry Kinematics Projectile Motion Acceleration Force Types of Acting Forces Circular Motion Torque Friction Center of Mass Moment of Inertia Power Trigonometry = the branch of mathematics that deals with the relations between the sides and angles of plane or spherical triangles • • • Used extensively in the process of designing the physical robot Triangular structures are much stronger than any polygon and are frequently used as frames and supports Removing too much material will begin to weaken the structure Kinematics PROS • • CONS Simple equations which require any 4 of 5 select variables in order to be solved Used for horizontal, projectile, and rotational motion Variables Δx v v0 a t • • • Must know the values for at least 4 variables Restricted to basic, ideal scenarios Acceleration must be constant EQUATIONS v = v0 + a*t Δx = v0*t + ½ a*t2 Δx = ½ (v0+ v)*t v2 = v02 + 2*a*Δx Projectile Motion = the motion an object experiences when the only force acting on it is gravity • • • • • Critical for games where game pieces are launched Allows for accurate, consistent shots Need to account for inconsistent variables o Deformation in resilience would play a large role in how an object's projectile motion changes over time, making shots inaccurate Uses simple equations which require values for Δy, v0, v, a, and t Important knowledge for designing, constructing, and programming the end effector Acceleration = the change in velocity during an interval of time • • Drivetrain Determines the ideal: o gearbox o combination of motors The acceleration for FRC robots needs to be very quick in order to reach top speeds immediately. • • • End Effector Critical to establish the speed of flywheels for shooting games Must be driver friendly (not too fast/slow) Deceleration of arm may be necessary to minimize stress/strain Force = any influence that causes an object to undergo a change in velocity or direction • • • • • F = Mass * Acceleration There are different types of forces and each one affects the robot differently Each force is considered a load and loads cause stress points across the robots frame and components Power to lift or push an object Particularly useful to calculate for hanging games Types of Acting Forces • • Static Load: Forces on a still object (weight of a robot) Dynamic Load: Forces in motion (force of robot's moving arm on the robot) Forces Continued • • • • Tension: When the ends of an object are pulled away from its center Compression: When the ends of an object are pushed towards its center Shear: Applied parallel or tangential to a face of a material Torsion: Occurs when an object, such as a bar with a circular or square cross section, is twisted Circular Motion = rotation along a circular path ac = vt2/r = r*w2 Fc = m *vt2/r = m*r*w2 • • • Relevant for all wheels on the robot Speed along the outside edge of the wheel can be found by multiplying RPMs by circumference. (this is known as tangential speed) This has an impact on wheel size in that the radius and distance travelled are directly proportional THIS DOES NOT MEAN BIGGER WHEELS ARE ALWAYS BETTER Torque = the tendency of a force to rotate an object about an axis, fulcrum, or pivot =∗ Torque is directly proportional to the radius Thus, the greater the radius, the larger the torque is necessary to produce the same force. Greater torque translates to greater pushing strength While large wheels may seem appealing, small wheels may be more advantageous • • • • Friction = the force which resists motion • • • • • All objects undergo friction, and friction generates HEAT Different types of wheels will behave differently with the carpet Some mechanisms will require grease or another lubricant to reduce friction and heat If friction between some objects is too high, they could bind together (i.e. gears) This causes inefficiencies. In some applications, increased friction could be beneficial such as wheel contact with the carpet, but more doesn't always mean better Center of Mass = A point representing the mean position of the matter in a body or system • • Keeping the center of mass nearest the center or the body, will not only help balance, but other things like reducing the turning radius and ensuring the weight is evenly distributed Keeping the center of mass low will minimize the risk of tipping over Other Examples 2013 Hanging 2012 Balancing 2009 Back heavy Moment of Inertia = a property of rotating bodies; the resistance to a change in angular velocity about an axis of rotation • • • Determines how quickly the wheel accelerates and how easily it maintains its angular velocity Must consider for all wheels & rollers Hollow cylinders have greater moments than solid cylinders (i.e. better suited for different purposes) Power = The rate at which energy is transferred, used, or transformed Power = Force * Distance / Time OR Power = Torque * Rotational Velocity FRC definition - how fast you can move something • • Many different motors can be used to accomplish the same task, but power determines how quickly any particular motor can perform the task Motors can be geared together and their power adds together. All motors can lift the same amount (assuming 100% power transfer efficiencies) - they just do it at different rates Efficiency in a system is never 100% (friction, heat, etc) Power Examples Greater power is needed when creating mechanisms which need to reach top speed quickly: Flywheels, drivetrains, elevators, arms When motors are paired together properly, the speed of an action is increased. 118's 2007 swerve - 4 CIM + 2 Fischer Price Questions? Sources & Links Power - http://www.instructables.com/id/Understanding-Motor-and-GearboxDesign/?ALLSTEPS https://www.khanacademy.org/science/physics http://mort11.org/ Definitions of all topics - www.wikipedia.org