“…One of its applications is used as power systems of elevator. Planetary gear trains were the subject of intensive research directed at kinematic analysis (Tsai,1985;Hsieh et al, 1989;Hsieh and Yan, 1992;Nelson and Cipra, 2005;Tsai and Huang, 2010), kinematic design (Hsieh , 1999;Hsu, 2002;Hwang, and Huang, 2005;Hsieh et al, 2006Hsieh et al, , 2008Karaivanov and Popov, 2008;Lu and.Duan, 2009;Hsieh, andTang, 2012, 2013), efficiency analysis (Castillo, 2002;Chen and Angeles, 2007;Lu and Duan, 2009;Golenko, 2009;Hsieh and Chen, 2011Hsieh andH.C. Tang, 2013, 2014), and patents (Takahashi , 1980;Klinger et al, 2002;Lin and Lin, 2004;Hsieh andChen, 2012, Hsieh et al, 2013).…”