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LinkJacobiMatrix

LinkJacobiMatrix[mx, vars]
calculates the Jacobian matrix of the homogeneous matrix mx with respect to generalized coordinate vector vars
  • LinkJacobiMatrix returns a matrix with the dimension of 6xn, where n is the number of the generalized coordinates.
  • With the help of the link Jacobian matrix one can calculate the translational and angular velocity of the point defined by the origin of the frame mx.
  • If the mx represent a frame attached to link and the generalized coordinate are the driving variables of the linkage, the link Jacobian matrix maps the driving variable velocities to the absolute velocities of link.
  • Jmx=(
    a1,1a1,2...a1,n
    a2,1a2,2...a2,n
    ...
    a6,1a6,2...a6,n
    )
  • (
    )=Jmx.(
    ), where
    Jmx: link jacobian matrix of mx
    : the velocity vector of the origin point of mx
    : the angular velocity of the link where the mx marker is attached.
Load the LinkageDesigner package
In[1]:=
Click for copyable input
Load the predefined crank-slider mechanism
In[2]:=
Click for copyable input
Out[2]=
Display the kinematic graph of the linkage
In[3]:=
Click for copyable input
Out[3]=
This returns the LLRF matrix of "Slider" link.
In[4]:=
Click for copyable input
Out[4]=
Calculate the link Jacobian matrix of mx with respect to the first three joint variables
In[5]:=
Click for copyable input
Out[5]//MatrixForm=