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GenerateInvKinEquations

GenerateInvKinEquations[linkage, endlink, startlink]
generates a list of starting equations of the inverse kinematic problem, which is generated from the target transformation matrix is equated with the placement transformation of the endlink's LLRF to the startlink's one
GenerateInvKinEquations[linkage, {endlink , mx1}, {startlink, mx2}]
returns a list of starting equations of the inverse kinematic problem, which is generated from the target transformation matrix is equated with the placement transformation of the mx1 to the mx2
  • The inverse kinematic problem : Given the target transformation matrix, that specify the desired placement of the endmarker relative to the startmarker. Find the relation, that express the driving variables as the function of target variables.
  • The elements of the target transformation matrix are the target variables. If the inverse kinematic problem is solvable the target variables became the independent variables of the linkage since the driving variables will be expressed as the explicit function of the target variables.
  • The target transformation matrix can be specified by the TargetMarker option. In case of TargetMarker→Automatic the following matrix is used as target transformation matrix
  • The list of staring equations are generated based on Paul's method. The initial equations are generated by equating the corresponding elements. is the homogeneous transformation between j and i link. Further equations are generated by pre-multiplying iteratively with the inverse of the consecutive matrices. The duplicates of resulted redundant equations are eliminated.
  • GenerateInvKinEquations function returns a list of redundant equations that is used by the template equation based solver. see PatternSolver
optiondefault valuedescription
TargetMarkerAutomaticSpecifies the target matrix of the inverse kinematic problem
EXAMPLESCLOSE ALL
Basic Examples   (1)
Load LinkageDesigner package.
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Define the four-bar mechanism
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Generate the starting set of equations of the loop closing constraint
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Try to solve equations for {2, 3} variables
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