The second type is realized
when different branches of the forward kinematics
problem converge, resulting in additional DOF at
the end-effector. Simultaneous occurrence of these
two kinds can be classified as the third type of singularity. Additionally, there also exist architectural
singularities, e.g. when the dimensions of the moving
and fixed platforms are comparable. Therefore,
special care should be taken in the design of these
manipulators to avoid the said singularities. It is
found that these singularities by reducing a certain
number of legs from the full kinematic chain and
carrying out a Jacobian analysis for the reduced
loop. The corresponding Jacobians are termed as
the intermediate Jacobians.