SEMESTER PROJECT - CORIOLIS–MA-EXCEL –WM –Page 1

  1. Joints A and D are fixed to the ground. Use the complex number method developed in class to derive the Loop Closure Equation –ABCDA-keep the Loop Closuer Equation in general form with all variables, including the input angle
  1. Separate into Real and Imag. Parts and label the Real equation as Eqn. (1) and the Imag. Eqn. as Eqn. (2) – Eqns. (1) and (2) are the position equations for the unknowns angle θ and distance r - Keep Eqs. (1) and (2) -in general form with all variables, including the input angle
  1. Solve the system of Eqs. (1) and (2) and simplify to obtain a single expression for angle θ and another single expression for distance r
  1. Take derivatives of Eqs. (1) and (2) to obtain the two velocity equations (3) and (4) – Keep Eqs. (3) and (4) in general form with all variables, including the input angle
  1. Solve Eqs. (3) and (4) and simplify to obtain a single expression for angular velocity θ Dot and to obtain a single expression for Sliding Velocity rDot
  1. Take derivatives of Eqs. (3) and (4) to obtain the two acceleration equations (5) and (6). Solve Eqs. (5) and (6) and simplify to obtain a single expression for angular acceleration θ DDot and to obtain a single expression for Sliding Acceleration rDDot

SEMESTER PROJECT - CORIOLIS –MA- EXCEL – WM –Page 2

  1. USE EXCEL TO DO THE FOLLOWING-
  1. Start angle  at 0 degrees – along line AD -and use increments of five degrees up to 360 degrees
  2. Calculate MA
  3. Calculate Coriolis Acceleration
  4. Calculate position of point E – RE vector
  5. Calculate velocity of point E – RE Dot vector
  6. Calculate acceleration of point E –REDDot vector
  7. Plot in SEPARATE graphs the items in Steps 2 through 6 above and the coupler curve– path of point E; these must be plotted in terms of the input angle ; each graph must be clear with proper labels, units for each axis, etc.
  1. USE WM TO DO THE FOLLOWING:

1Start bar AB at an angle of 6 degrees where  = 0 and run for one revolution

  1. Measure angle (angle from WM – 6 degrees)
  2. Measure and export appropriate quantities into an Excel file;within Excel calculate MA, Coriolis Acceleration and position, velocity and acceleration of point E
  3. Plot MA, Coriolis Acceleration, and position, coupler curve, velocity and acceleration of point Ein EXCEL- everything must be plotted in terms of the input angle ; each graph must be clear with proper labels, units for each axis, etc.
  1. COMPARE PLOTS FROM THE TWO METHODS TO INSURE THAT RESULTS ARE CORRECT