CalculateInverseDynamics

CalculateInverseDynamics[linkage]
Calculates the generalized forces of the mechanism, when it kinetically determined in such a way that the driving velocities are constant and the driving accelerations are zero.
  • In case of kinetically driven mechanism the time parametrization of the generalized coordinates ( driving variables) is given. Therefore the first and second derivative of these function can be calculated and substituted into the Lagrange's equation. The Lagrange's equations, which originally a second order ordinary differential equations, become algebraic equation.
  • CalculateInverseDynamics assumes a special time parametrization of the generalized coordinates, namely generalized coordinates ( or driving variables) linear with constant velocity.
  • qi[t]=vi*t , where
  • qi is the i-th driving variable
  • vi is the i-th driving velocity
Load LinkageDesigner package
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Convert the linage into time dependent linkage
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Calculate mass properties of the linkage. Uniform density of 70 kg/m^3 is used
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Calculate the generalized forces based on the inverse dynamics of the pendulum
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Calculate the substitution values for one complete rotation
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Show the calculated torque function of the rotational joint, which is the generalized force of the driving variable
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Define the calculated torque as an interpolated function of the 1 driving variable
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Copy LinkageData of pend to pend1 variable
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Assign the interpolated torque function to act on link1 of the pendulum
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Solve the Lagrangian's equation for the pendulum driven by the calculated torque function, for one whole rotation
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Plot the time-driving variable function for [0,2] interval
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Animate the movement of the linkage
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Calculate the movement of the pendulum if a constant torque is applied.
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Solve the Lagrangian's equation for the pendulum driven by the constant torque
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Plot the time-driving variable function for [0,2] interval
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Animate the linkage
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