MKM301 THEORY OF MACHINES TERM HOMEWORK FALL 2024-2025 12 m/s ky Due Date: January 10, 2025 (Late submissions will not be accepted!) Subject: A Full Kinematic Analysis of a Planar Linkage Mechanism Questions: 1) (10P) Please choose a planar linkage mechanism having not more than 2 degrees of freedom then concisely explain its function in practice. You may use real images of the mechanism and its major components to improve your explanation. 2) (20P) Draw simplified sketch (skeleton diagram) of the mechanism. Label the number of links (n), joints (j) and determine the connectivity sum (Σfi). Determine the degree of freedom (DOF) of the mechanism. Show all necessary fixed parameters (or dimensions) and joint variables clearly on the sketch. 3) (20P) Find the number of independent loops. Select the joint(s) to be virtually disconnected and write down the loop closure equations both as a vector equation and as a complex equation. Make a list of fixed parameters and the joint variables that you have used. Use Oi & sij for the joint variables; |AB|, |BCI, etc. for the constant lengths and ai, ẞi etc. for the constant angles. 4) (30P) a) Derive the analytical expressions for position variables (e.g. 02, 04, 05 or s6) in terms of the input variables for the closure. b) Derive the analytical expressions for the velocity variables in terms of the input velocity, position variables and fixed dimensions. c) Derive the analytical expressions for the acceleration variables in terms of the input angular velocity, position and velocity variables and fixed dimensions. 5) (20P) Clearly express input variables of the velocity and acceleration considering operating conditions of the mechanism in practise then generate a curve for the path, velocity and acceleration for the motion of the output link of the mechanism and plot them using a computer software. Important Notes: - You can use linsolve or solve commands of MATLAB to solve symbolic linear equations. The reports can be prepared either using MS Office Word or worksheets with a proper handwriting. Organize a cover paper for the submission including your name, student number and title of the report consistent with the chosen mechanism. - At each step of the full kinematic analysis report, please provide necessary explanations. The reports will be submitted online to ibrahimkocabas@eskisehir.edu.tr as a single pdf file.