Consider the inverted slider-crank mechanism shown, where a spring is connected between the tip of link...

 

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Consider the inverted slider-crank mechanism shown, where a spring is connected between the tip of link (3), point B, and point R on the ground. The data for this system are given as: C L = OA=0.20, L = QB = 0.8 m a = b =0.4, c = 0.5 m m = 0.1, m = 0.2, m = 0.3 kg J = 0.01, J = 0.05, J = 0.02 kg.m k = 1,000 N/m, L = 0.3 m Gravity acts in the negative y direction. A driver motor rotates body (1) at a constant speed of 2 rad/s CCW. (Figure is not to scale or in proportion to the given dimensions.) b a O R X B (a) Construct the constraint equations for a kinematic analysis of this mechanism. Develop necessary expressions for determining the coordinates of the secondary point B and the accelerations of the mass centers. Construct the equations of motion for the complete system. (b) Revise your MATLAB program from HW-5 (or develop a new program) to perform a complete kinematic analysis of this inverted slider-crank. Add the expressions for the kinematics of the secondary points B and the mass centers to the program. (c) Add the necessary matrices and arrays for the equations of motion to the program (refer to Example 6.6 and the corresponding MATLAB program). (d) Provide statement to solve the equations of motion in order to determine the applied torque of the driver motor for any given value of the crank angle. (e) Perform a simulation for a complete rotation of the crank at increments of 5 degrees. Plot the angular velocity of link (3) versus the crank angle. What do you observe? Plot the torque of the drive motor versus the crank angle. Submit the results with your complete program containing all the files. Consider the inverted slider-crank mechanism shown, where a spring is connected between the tip of link (3), point B, and point R on the ground. The data for this system are given as: C L = OA=0.20, L = QB = 0.8 m a = b =0.4, c = 0.5 m m = 0.1, m = 0.2, m = 0.3 kg J = 0.01, J = 0.05, J = 0.02 kg.m k = 1,000 N/m, L = 0.3 m Gravity acts in the negative y direction. A driver motor rotates body (1) at a constant speed of 2 rad/s CCW. (Figure is not to scale or in proportion to the given dimensions.) b a O R X B (a) Construct the constraint equations for a kinematic analysis of this mechanism. Develop necessary expressions for determining the coordinates of the secondary point B and the accelerations of the mass centers. Construct the equations of motion for the complete system. (b) Revise your MATLAB program from HW-5 (or develop a new program) to perform a complete kinematic analysis of this inverted slider-crank. Add the expressions for the kinematics of the secondary points B and the mass centers to the program. (c) Add the necessary matrices and arrays for the equations of motion to the program (refer to Example 6.6 and the corresponding MATLAB program). (d) Provide statement to solve the equations of motion in order to determine the applied torque of the driver motor for any given value of the crank angle. (e) Perform a simulation for a complete rotation of the crank at increments of 5 degrees. Plot the angular velocity of link (3) versus the crank angle. What do you observe? Plot the torque of the drive motor versus the crank angle. Submit the results with your complete program containing all the files.

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Solutions Step 1 a Constraint equations for a kinematic analysis of the inverted slidercrank mechani... View the full answer