Theory of Machines Assignment 1_24 Mathematics Wire frame The figure shows a mechanism which consists of two loops. The mechanism is driven by link 2 which is attached to the inertial frame through a revolute joint at O. There are revolute joints at A, B, C and D. Link 5 is attached to a vertical slider through a revolute joint at E. The vertical distance between O and E is S. Joint D is midway between B and C The dimensions, in mm are: L2 15 L3 150 L4 60 L5 75 d 60 e 20 f 40 Link 2 makes an angle of 100° to the horizontal for the position shown. Use a vector q = 04 05 to define the coordinate of the mechanism. 1. Use the loop closure method to derive the constraint equations for the horizontal and vertical components of the position. Append a fifth constraint equation which specifies the angle 02 to be 100°. 2. Differentiate the constraint equations to give the Jacobian matrix 3. Give a vector of x-calculations and y-calculations that can be used in a plot frame for drawing a wire frame of the mechanism. The values must be able to draw the mechanism as a single graph without lifting the ‘pen'. Write an Octave functions to: 1. Calculate the Jacobian 2. Use the Newton Raphson method to solve for the co-ordinate to an accuracy of 10-6. 3. Calculate the value of the @(g) functions which form the constraint equations. 4. Plot the wire frame of the mechanism. Write an Octave script that will draw the wire frame of the mechanism in the position shown using the functions defined. Results must be presented in SI units. The functions must be stored in separate m-files so they can be called from other scripts. TO2 S 03 Submit: 1. A pdf of your mathematics 10 2. All the necessary m-files 10 3. A pdf containing the output of your script 5 B 3 d 4 A D 2 0 e 5 C S 1 E f Figure: Mechanism (Not to Scale)