Xtreme Robot Olympiad Adventure Racing Peter Laz Associate Professor Department of Engineering University of Denver Current Standings Team Points Green, Aqua 50 Gold, Blue 47 Gray, Yellow, Orange, Teacher 44 Red, Purple 41 Robot Adventure Racing • Develop your own original design • Choose a new body structure • Change the gears and wheels • Additional materials will be available for “purchase” • Each team has a “virtual budget” of $25 • All team members will drive • Score is the average time for your team members • Additional time bonus for a hanging robot • Teams will have 1 minute to get their robot to hang from the pull-up bar Outline • • • • Design tradeoffs Vehicle configurations Forces and Torques Gears • Speed and torque • Wheels Vehicle Configurations • Subsystems • Structure • Steering • Drive train • Considerations • • • • Stability Maneuverability Power transmission – torque versus speed Implementation • • • • Responsiveness (steering/oversteering) Programming Weight distribution Cost Vehicle Configurations Many Questions: • How many wheels? 2, 3, 4 • Two wheel or four wheel drive? • Front wheel drive or rear wheel drive? • How many motors? • How will you turn? Vehicle Configurations • All wheel drive and all wheel steering may be too complicated. www.howstuffworks.com 2-Wheel Configurations Front Wheel Drive Rear Steer = Steering = Driven Rear Wheel Drive Front Steer Front Wheel Drive Front Steer Two wheel configurations may be unstable 3-Wheel Configurations Front Wheel Drive Rear Steer = Steering = Driven Rear Wheel Drive Front Steer Front Wheel Drive Front Steer 4-Wheel Configurations Front Wheel Drive Rear Steer Rear Wheel Drive Front Steer Front Wheel Drive Front Steer All Wheel Drive Need for differentials and/or steering linkages = Steering = Driven Tank drive has difficulties going straight as motors are not identical. Engineering Fundamentals Force • Units of force • Newtons (N = kg*m/s2) • Pounds (lb = lb*ft/s2) SI system US system • Force = mass * acceleration • Weight = mass*g • Mass (kg), g = 9.81 m/s2 • Mass (slugs), g = 32.2 ft/s2 SI system US system Torque A torque or moment is equal to a force x distance at which it acts T r F F r = perpendicular distance Torque The direction a torque acts is determined by the right hand rule. • Point your hand in the direction of r • Then bend your fingers in the direction of F • Your thumb points to the direction of the torque For your unit vectors: but note: î ĵ k̂ î ĵ k̂ î î 0 ĵ î k̂ ĵ î k̂ ĵ ĵ 0 Exercise Find the magnitude and direction of the torque for each of the conditions a. c. r 2 î F 6 ĵ r 2 î F 2 î 6 ĵ b. r 2 î F 6 ĵ Sir Isaac Newton (1642-1727) Three Laws of Mechanics 1. A body continues in its state of rest or motion until a force is applied 2. The change of motion is proportional to the force applied 3. For every action there is an equal and opposite reaction Static Equilibrium • Newton’s First Law • The sum of the forces and moments acting on a body are zero (0) F 0 Fx 0 Fy 0 Mo 0 Levers • Consist of 3 parts • Effort • Resistance • Fulcrum (pivot point) Effort Force W Levers • First class lever – fulcrum between the weight and the effort Effort Force W • What happens to the effort • if the fulcrum moves to the left? • if the fulcrum moves to the right? Levers • Second class lever W Effort Force • Third class lever W Effort Force Static Equilibrium • Moments caused by effort and resistance are equal Mfulcrum 0 Mfulcrum reffort Feffort rresist Fresist reffortFeffort rresistFresist Mechanical Advantage • Measure of the ability of a machine to amplify force Resistance (Force) M.A. = Effort (Force) Effort Arm M.A. = Resistance Arm Gears • Some examples include • • • • Can opener Cork screw Transmission on your car Bicycle • Gears are used to • Change the direction of motion • Increase or decrease speed • Increase or decrease torque • Gears are commonly used in power transmission applications because of their high efficiency (~98%) Gears Configurations • Spur gears • Wheels with mating teeth • Rack and pinion gears • Changes rotational motion to linear motion • Worm gears • Bevel gears • Connects shafts lying at angles Gear Ratio • A gear will rotate with an angular velocity (w) with units of radians/second • Gears have teeth that must mesh • Same pitch = same distance between teeth • There is a fixed ratio between the teeth and the gear radius N1 r1 N2 r2 N = Number of teeth, r = radius Gear Ratio - Velocity • Velocity of pitch point C on both bodies must be equal w2 w1 Vc r1 w1 r2 w 2 w2 w1 r1 r2 C N1 N2 w= angular velocity Driver or Pinion Driven Gear Ratio - Torque • Force of gear 1 on gear 2 is equal and opposite to force of gear 2 on gear 1 F w2 w1 T1 r1 r1 r2 w1 T1 T2 r2 N1 N2 C w = angular velocity T1 T2 Driver or Pinion Driven T2 w2 Gear Problems • Master Equation w2 w1 r1 r2 N1 N2 T1 T2 • Small gear to large gear • Slower angular velocity, increased torque • Large gear to small gear • Faster angular velocity, reduced torque Exercise w2 What are the gear ratios? Let: rgreen = 6 inches rblue = 10 inches rred = 15 inches wgreen = 10 rad/sec What is wred? Is Tred < or > Tgreen? w1 w1 Exercise • What is the gear ratio for the squarebot? • Does it increase or decrease the speed of the motor? • Does it increase or decrease the torque of the motor Motor Specification • Free speed • 100 rpm @ 7.5 volts • Stall Torque • 6.5 in-lbs Gear Design Decisions • Which gears will you choose for your design? • What is the best ratio? • Be careful not to overload your motor. http://www.vexlabs.com/vexrobotics-motor-kit.shtml Wheel Size? • Large wheels • Faster top speed, slower acceleration • Small wheels • Slower top speed, faster acceleration • Which wheel will do better for rough terrain? 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