This paper presents a design for stair-climbing using a
wheel that can split into segments and walk up stairs or surmount
other obstacles often found where humans traverse, while still being
able to retain a perfectly round shape for traveling on smooth ground.
Using this change of configuration, staircases with a wide range of
dimensions can be covered efficiently and safely. The design, named
Umbrella Wheel, can consist of as many wheel segments as desired,
and as few as two. A smaller or higher number of wheel segments
has advantages and disadvantages depending on the specific situation.
Modeling the trajectory of the wheel when as it ascends or descends
stairs is given and the results are analyzed.