Forces a = cos-1(Fx /FR) B = cos-1(FY /FR) Y = cos-1(Fz/FR) Force Equilibrium 1. Free Body Diagram 2. Coordinates 3. Position Vectors 4. Unit Vectors 5. Force Components 6. Equations of Equilibrium for Forces 7. Solutions NOTE -- > g=9.81 m/s^2 or g=32.2 ft/s^2 Moments (MR) .= ??+?(FXF) M IS EXISTING MOMENTS, R IS THE POSITION VECTOR FROM MOMENT LOCATION TO FORCE Replace Couple Moment with Wrench 1. Free Body Diagram 2. Find Total Force Components and Magnitude for UF 3. Use Cross Products to find MR · If necessary, position vector components can be variables 4. Use MR = M * UF to Solve System Moment Equilibrium 1. Free Body Diagram . Determine and draw reaction forces and moments 2. Coordinates 3. Position Vectors 4. Unit Vectors 5. Forces 6. Moments 7. Equations of Equilibrium for Forces and Moments · Include reaction forces and moments 8. Solutions
Friction Fs = HSN N IS THE NORMAL FORCE. TRUE FOR IMPENDING SLIDING. Fk = ??? N IS THE FORMAL FORCE x = Ph / W X IS DISTANCE FROM CENTER TO MOMENT ORIGIN, P IS APPLIED FORCE, AND W IS LOAD/FORCE OF GRAVITY x = 1/2 L X IS DISTANCE FROM CENTER TO MOMENT ORIGIN, L IS BOTTOM LENGTH OF OBJECT. TRUE FOR IMPENDING TIPPING. FRICTION: STATIC AND IMPENDING MOTION 1. Free Body Diagrams for Both Objects 2. Force Equilibrium Equations · Include reaction forces if applicable · Do easy calculations to remove unknowns 3. Moment Equilibrium Equations (not for wedges) · Calculate moments about the easiest origin · Counter-clockwise is positive · Do easy calculations to remove unknowns 4. Make Assumptions (if necessary to remove more unknowns) 5. System of Equations 6. Solutions 7. Verify Solutions
Reactions Types of Connection Reaction Number of Unknowns (1) F cable (2) One unknown. The reaction is a force which acts away from the member in the known direction of the cable. One unknown. The reaction is a force which acts perpendicular to the surface at the point of contact. F smooth surface support (3) roller Types of Connection One unknown. The reaction is a force which acts perpendicular to the surface at the point of contact. F Reaction Number of Unknowns (4) F ball and socket (5) single journal bearing Three unknowns. The reactions are three rectangular force components. F F M. Four unknowns. The reactions are two force and two couple-moment components which act perpendicular to the shaft. Note: The couple moments are generally not applied if the body is supported elsewhere. See the examples. F F. by a support that resists moments about the x and = axes of the bearing (e.g. by another bearing)