Mechanical system is shown in the figure. Torque, T(t), is given as an input which is applied onto the disc and linear displacement of the cart, x(t), is given as an output for the system. The other parameters and positive directions are given in the figure, also: M is the mass of the cart, J is the inertia of the disk, k is a linear and kT is a torsional spring constants, b is a linear damping constant, β is an angular displacement of the disk. a) At first, draw the necessary free-body diagrams (FBD’s) for the system. Then, identifying the forces with given elements (parameters) in the figure, write all elemental equations used in the FBD’s. [ Note: Do not ignore the force which shows up on the contact point between the cart and the disc. Note 2: Please pay attention to the positive and negative signs that indicate the direction.] b) Obtain the equation of motion (EoM) for the system in terms of input & output using Newton’s Laws (i.e. *Continuity Eqn’s) c) Take Laplace transform of all elemental & continuity eqn’s and EoM. Then, find the transfer function (TF) of the system.
the disc and linear displacement of the cart, x(t), is given as an output for the system. The other
parameters and positive directions are given in the figure, also:
M is the mass of the cart, J is the inertia of the disk, k is a linear and kT is a torsional spring
constants, b is a linear damping constant, β is an angular displacement of the disk.
a) At first, draw the necessary free-body diagrams (FBD’s) for the system. Then, identifying the
forces with given elements (parameters) in the figure, write all elemental equations used in
the FBD’s. [ Note: Do not ignore the force which shows up on the contact point between the
cart and the disc. Note 2: Please pay attention to the positive and negative signs that indicate
the direction.]
b) Obtain the equation of motion (EoM) for the system in terms of input & output using
Newton’s Laws (i.e. *Continuity Eqn’s)
c) Take Laplace transform of all elemental & continuity eqn’s and EoM. Then, find the transfer
function (TF) of the system.
d) Draw the block diagram of the system using Laplace transforms of the equations in part (c).
[ Note: Start with the equation containing the highest derivative of the output.]
e) Simplify the block diagram using with “Block Diagram Algebra” or “Analytical**” Method
to find the TF. Compare your results which you obtained in part (c) & (e).
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 8 images
