Yüca, GülsümYaylı, Yusuf2023-10-192023-10-1920231225-293X2288-6176https:/dx.doi.org10.5831/HMJ.2023.45.2.198https://hdl.handle.net/20.500.12451/11188In the present paper, we investigate homothetic motions de-termined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable prop-erties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.eninfo:eu-repo/semantics/closedAccessHomothetic MotionHamilton OperatorQuaternionLorentzian SpaceDual SpacekinematicsArticle45219821410.5831/HMJ.2023.45.2.198N/A