Analysis of Kinematic Chains
The constraint equations of a kinematic chain couple the range of movement allowed at each joint to the dimensions of the links in the chain, and form algebraic equations that are solved to determine the configuration of the chain associated with specific values of input parameters, called degrees of freedom.
The constraint equations for a kinematic chain are obtained using rigid transformations to characterize the relative movement allowed at each joint and separate rigid transformations to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of n links connected in series has the kinematic equations,
where is the transformation locating the end-link---notice that the chain includes a "zeroth" link consisting of the ground frame to which it is attached. These equations are called the forward kinematics equations of the serial chain.
Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations.
The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors:
- Its topology: a serial chain, a parallel manipulator, a tree structure, or a graph.
- Its geometrical form: how are neighbouring joints spatially connected to each other?
Explanation:-
Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system.
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