Question
Please answer each question clearly and show your steps for best answer!
The figure defines the following vectors: A is the crank (length L1) B is the connecting rod or coupler (length L2) is the "fixed" link (length X(t)). In addition: S = X - L2 is the slider (or piston ) stroke or displacement theta 1(t) is the crank angle write the kutzbach criterion, identifying the terms, and predict the mobility, m, of this mechanism. What is the magnitude of total stroke |S| of the slider in terms of the constant parameters? Comment on any necessary practical aspects of the ratio L2/L1 (for example, what if L2 is shorter than L1) and consider this for various crank angles. What does the Grahof's law require? Write the kinematic loop closure equation (a) in terms of the vectors A, B & C and (b) in terms of L1, L2, X, theta 1 & theta 2 (note 2 eqns are required). Assuming theta 1 is known at some instant, identify the known and unknown magnitudes and directions of A, B & C and solve for the unknowns in terms of the given parameters using (a) trigonometry and (b) the chace solutions. Derive an expression for S in terms of LI, L2 and theta 1. eliminating theta 2. Assuming X (or S) is known at some instant, identify the known and unknown magnitudes and directions of A, B & C and solve for the unknowns in terms of the given parameters using (a) trigonometry and (b) the chace solutions. Derive an expression for dS/dt (the slider vel) in terms of L1, L2 and theta 1.
Explanation / Answer
1)Kutzbach criteria is given by: 3(n-1)-2*L-h = no of degrees of freedom where n= number of links L=no. of lower pairs h=no. of higher pairs.
here n=4 l=4 (3 revolute 1 sliding)
degree of freedom =1
2)Magnitude to total stroke S= 2*L1
3)If L2 is shorter than L1 that means the crank is bigger than the connecting rod. the motion of the piston will not be linear along a line instead it will revovle about the crank-frame joint.