Calculates the required input torque and the magnitudes

Assignment Help MATLAB Programming
Reference no: EM13841236

Consider the planar linkage shown below. The crank (link with length R) will turn counter-clockwise with a constant angular velocity (θ`).

The slider will experience a force (P) of 100 N directed to the left. Your task is to write a MATLAB program that

(a) Calculates the required input torque (T) and the magnitudes of the pin reaction forces (A, B, and C, along both x and y directions) for two full revolutions (0 ≤ θ ≤ 4Π) of the crank.

(b) You will then use your program to determine how changing the dimension H changes the average magnitudes of the pin reaction forces (refer to the free body diagram for the locations of these pins).

2342_Calculate the required input torque.png

The first task is to determine the angle Φ and the slider position s given the crank angle θ The constraint equations that must be satisfied are:

Rsin(θ)+ Lsin(Φ)= H (1)

Rcos(θ)+ Lcos(Φ) = s (2)

You are required to solve these nonlinear equations for the unknowns the angle Φ and s using the Newton-Raphson method (as used in HW3).

The next task is to solve for the (first and second) time derivatives of Φ and s, given θ (whose value is a constant, see in the figure on page 1). Equations (1) and (2) may be differentiated to obtain the following linear system of equations. You may use the MATLAB backslash operator "\"' to solve this set of equations.

1922_Calculate the required input torque1.png

The next step is to consider the free body diagrams and obtain the corresponding dynamic equations. The free body diagram is below. Note that we are neglecting friction on the slider.

182_Calculate the required input torque2.png

After simplification, the resulting dynamical equations in terms of the unknown reactions (Ax, Ax, Bx, By, Cx, Cy) and torque (T) can be expressed in matrix form as:

1812_Calculate the required input torque3.png

which can be solved using the MATLAB backslash operator "\", by taking the values for the coefficient matrix and right-hand-side vector from the above. Here, the link masses and moment of inertia are

m1 = 15 kg, m2 = 30 kg, m3 = 10 kg. 12 = (m2L2)/12.

In the above matrix, we use the following vectors

11_Calculate the required input torque4.png

Turn in a brief report containing the following:

(i) Title Page, including the title of the project and your name

(ii) Introduction and Objectives section

(iii) Program Design section (describe your program and the functions you used). Include all your M-files.

(iv) Results section, including properly labeled plots for the case where H = 0.25 m:

a. Φ and s vs. θ
b. Φ' and s' vs. θ
c. Φ" and s" vs. θ
d. |A|,|B|,|C|, and T vs. θ

(v) A single plot displaying the average value of the magnitudes of the three pin reaction forces (A, B, and over the complete cycle for the range -0.6 ≤ H ≤ 0.6 m. Results for each pin should be displayed differently (for example. use a different color or a different line type). Include a legend on the plot to label the results for the three different pins.

(vi) Discussion of results, including your conclusion from part (v).

Verified Expert

Reference no: EM13841236

Matlab program which will determine your vehicle fuel usage

Create a MATLAB program which will determine your vehicle fuel usage (MPG, miles/gallon) rating for a user defined number of trips ('for' repetition structure).

Determine the range of k for stability

Determine the range of K for stability. Develop an m-file to calculate the closed-loop poles for K from 0 to 5 with an increment of 0.1 (you may want to use the for loop in MA

Write a script that will prompt the user for the two areas

Write a script that will prompt the user for the two areas in square feet, and will print whether the velocity at the second point increases, decreases, or remains the same

Write a matlab code that plots the phase portrait of system

Write a MATLAB code that plots the phase portrait of the system. The values of the parameters r1, r2, K1, K2 are fixed and to be extracted from your matriculation number and y

Evaluate the function at a range of x values

Write a function file, that accepts values of x as inputs and outputs the value of y when the input is passed through the following function. Evaluate the function at a range

How spectrograms can be used in non-stationary signals

Use calculations and/or your conceptual understanding of spectra to predict what you'd expect the spectrum of this signal to look like. Confirm this hypothesis by again usin

Find the laplace transform of the functions

Find the solution of the differential equation - Find the Laplace transform - Find the Laplace transforms of the functions - Using Matlab and Laplace transform, find the solut

Calculate x - y using canonical forms parametric solution

Write a Sci/Matlab function that returns the function values and the Jacobian needed for Newton's method - show graphically how the intersection point of the two equations var

Reviews

Write a Review

 
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd