INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.13, sa.1, ss.107-115, 2020 (ESCI)
In this work, the exponential and the Cayley maps, from the Lie algebra se(z) of the planar motion group S E (2), to the group itself are studied. The comparison between these maps on S E (2) is given by using the Rodrigues vector. A three joint mechanism is discussed as an application.