Minimal line representation

Denavit–Hartenberg band coordinates

Main article: Denavit–Hartenberg parameters

Jaques Denavit and Richard S. Hartenberg presented the aboriginal basal representation for a band which is now broadly used. The accepted accustomed amid two curve was the capital geometric abstraction that accustomed Denavit and Hartenberg to acquisition a basal representation. Engineers use the Denavit–Hartenberg convention(D–H) to advice them call the positions of links and joints unambiguously. Every hotlink gets its own alike system. There are a few rules to accede in allotment the alike system:

the -axis is in the administration of the collective axis

the -axis is alongside to the accepted normal:

If there is no altered accepted accustomed (parallel axes), again (below) is a chargeless parameter.

the -axis follows from the - and -axis by allotment it to be a right-handed alike system.

Once the alike frames are determined, inter-link transformations are abnormally declared by the afterward four parameters:

: bend about antecedent , from old to new

: account forth antecedent to the accepted normal

: breadth of the accepted accustomed (aka , but if application this notation, do not abash with ). Assuming a revolute joint, this is the ambit about antecedent .

: bend about accepted normal, from old arbor to new axis

editHayati–Roberts band coordinates

The Hayati–Roberts band representation, denoted , is addition basal band representation, with parameters:

and are the and apparatus of a assemblage administration agent on the line. This claim eliminates the charge for a component, back

and are the coordinates of the circle point of the band with the even through the agent of the apple advertence frame, and accustomed to the line. The advertence anatomy on this accustomed even has the aforementioned agent as the apple advertence frame, and its and anatomy axes are images of the apple frame's and axes through alongside bump forth the line.

This representation is altered for a directed line. The alike singularities are altered from the DH singularities: it has singularities if the band becomes alongside to either the or arbor of the apple frame.