1. Modified Schedule 1:00-2:00 Lecture: Engineering Fundamentals 2:00-3:00 Final Vehicle Modifications 3:00-3:30 Break 3:30-5:00 Soccer Competition 5:00-6:00 Design Planning (Adventure Racing)

2. Xtreme Robot Olympiad Engineering Fundamentals Peter Laz Associate Professor Department of Engineering University of Denver

3. Outline Vectors Forces Torque Mechanical Advantage Levers Gears

4. Scalars versus Vectors A Scalar has a magnitude (no direction) Examples: speed, time, mass Notation: s, t, m A Vector has both magnitude and direction Examples: distance, velocity, acceleration, weight, force Notation:

5. Unit Vectors y Unit vectors have magnitudes = 1 and directions along the coordinate axes x

6. Vector Components A vector can be broken into components Use Trigonometry !!! y AxAx AyAy x A 

7. Vector Components A vector has magnitude and direction y AxAx AyAy x A 

8. Exercise 1.Determine the components A x and A y if the magnitude A = 80 N and  = -40° 2. What are the magnitudes and directions of the vectors?

9. Vector Addition and Subtraction Two Vectors Vector Addition add components in the same direction

10. Vector Addition and Subtraction Vector Subtraction subtract components in the same direction

11. Multiplication by a Scalar Multiplication by a scalar multiply each component by the scalar

12. Exercise Two Vectors Find the following a. b. c.

13. Force Units of force Newtons (N = kg*m/s 2 ) SI system Pounds (lb = lb*ft/s 2 )US system Force = mass * acceleration Weight = mass*g Mass (kg), g = 9.81 m/s 2 SI system Mass (slugs), g = 32.2 ft/s 2 US system

14. Torque A torque or moment is equal to a force x distance at which it acts = perpendicular distance

15. 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:

16. Exercise Find the magnitude and direction of the torque for each of the conditions a. b. c.

17. 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

18. Static Equilibrium Newton’s First Law The sum of the forces and moments acting on a body are zero (0)

19. Levers Consist of three parts Effort Resistance Fulcrum (pivot point) W Effort Force

20. Levers First class lever – fulcrum between the weight and the effort What happens to the effort if the fulcrum moves to the left? if the fulcrum moves to the right? W Effort Force

21. Levers Second class lever Third class lever W Effort Force W

22. Static Equilibrium Moments caused by effort and resistance are equal

23. Mechanical Advantage Measure of the ability of a machine to amplify force M.A. = Resistance (Force) Effort (Force) M.A. = Effort Arm Resistance Arm

24. 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%)

25. 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

26. Gear Ratio A gear will rotate with an angular velocity (  ) 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 N = Number of teeth, r = radius

27. Gear Ratio - Velocity Velocity of pitch point C on both bodies must be equal Driven Driver or Pinion C 11 22  = angular velocity

28. Gear Ratio - Torque Force of gear 1 on gear 2 is equal and opposite to force of gear 2 on gear 1 Driven Driver or Pinion C 11 22  = angular velocity T1T1 T2T2

29. Gear Problems Master equation Small gear to large gear Slower angular velocity, increased torque Large gear to small gear Faster angular velocity, reduced torque

30. Exercise What are the gear ratios? Let: r green = 6 inches r blue = 10 inches r red = 15 inches  green = 10 rad/sec What is  red ? Is T red T green ? 11 22 11

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