Forward kinematics

The direct kinematics or forward transformation is a term used in robotics. It deals with the question of how from the joint angles of the arm members of an industrial robot pose ( position and orientation) of the end effector (English: Tool Center Point, TCP) can be determined with respect to the base coordinate system (UCS ). It is the objective counterpart of the inverse kinematics.

With serial arrangements of the structural components and joints, such as in many industrial robots, the kinematics can be directly calculated through a simple matrix multiplication of the Denavit -Hartenberg matrices ( see Denavit -Hartenberg transformation):

Position and orientation of the TCP coordinate system can be expressed relative to the base coordinate system with the help of this matrix now, which is equivalent to the solution of the direct kinematic problem.

This calculation can also be done analytically and therefore in real time to control machinery. For machines or robots with parallel kinematic structure, which can not be described by Denavit -Hartenberg parameters is not possible, an analytical solution of direct kinematics in general. Analytical solutions exist only under strict geometric conditions.

The correlations tries to clarify the following picture:

It should be noted that only in the case of the same number of parameters (that is, as a rule 6) is a one-one mapping is possible. Otherwise, one speaks of redundant kinematics.

  • Robotics
  • Engineering Mechanics
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