1. Deals with the effect of forces on three-dimensional rigid bodies. Approach is the similar to 2-D Forces will be resolved into 3 components Moments are computed relative to an axis. Spatial Mechanics Section 3

2. Components given the line of action. Use proportions where: Force Components F dzdz x y z dydy dxdx d

3. Problem 3-1 Determine the x, y and z components of the 300 lb force. 300 lbs 4 ft 5 ft 6 ft x y z

4. Components given directional angles. Resolve into vertical (y) and horizontal components Resolve horizontal component into x & z component Force Components x y z F 11 22

5. Problem 3-4 Determine the x, y and z components of the 50 lb force. x y z 50 lb. 55 0 40 0

6. Static Equilibrium Machine component is in static equilibrium when the combination of all forces, in all three directions, is zero.  F x = 0  F y = 0  F z = 0

7. Static Equilibrium In addition, the net effect of all moments, about all axes (with any arbitrary origin), must also result in zero.  x = 0  y = 0  z = 0

8. Problem 3-7 The 400 lb plate is supported by the three cables. Determine the tension in each cable. B A C 2’ 4’ 3’ 1’

9. Problem 3-10 Determine the forces at A and B to keep the bracket in equilibrium. x y z 150 lbs 25 0 40 0 4 in 2 in 1 in A B 2 in

10. Problem 3-12 Determine the torque required from the flexible coupling to drive the following shaft. Also, determine the bearing reactions.

11. Problem 3-13 Determine the required force P and the bearing reactions at A and B, to keep the winch in equilibrium. X Y Z 12 in 8 in 10 in 6 in 5 in 600 lb P A B

12. Problem Determine the required force P and the bearing reactions at A and B, to keep the winch in equilibrium. P 12 in 8 in 10 in 6 in 5 in 600 lb A B 75 0 65 0