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Yet there is no established approach to the modeling of complex mechanisms possessing multiple kinematic loops. For such mechanisms, it is crucial to incorporate the kinematic topology within the modeling in a consistent and systematic way. To this end, in this paper a kinematic model graph is introduced that gives rise to an ordering of the joints within a mechanism and thus allows to systematically apply established kinematics formulations. It naturally gives rise to topologically independent loops and thus to loop closure constraints. Geometric constraints as well as velocity and acceleration constraints are formulated in terms of joint screws. An extension to higher order loop constraints is presented. It is briefly discussed how the topology representation can be used to amend structural mobility criteria.<\/jats:p>","DOI":"10.1017\/s0263574718000619","type":"journal-article","created":{"date-parts":[[2018,8,2]],"date-time":"2018-08-02T10:05:18Z","timestamp":1533204318000},"page":"1641-1663","source":"Crossref","is-referenced-by-count":32,"title":["Kinematic topology and constraints of multi-loop linkages"],"prefix":"10.1017","volume":"36","author":[{"given":"Andreas","family":"M\u00fcller","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2018,8,2]]},"reference":[{"key":"S0263574718000619_ref45","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574714000149"},{"key":"S0263574718000619_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(81)90033-1"},{"key":"S0263574718000619_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.07.104"},{"key":"S0263574718000619_ref6","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198562450.001.0001","volume-title":"Robots and Screw Theory: Applications of Kinematics and Statics to Robotics","author":"Davidson","year":"2004"},{"key":"S0263574718000619_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0031048"},{"key":"S0263574718000619_ref17","doi-asserted-by":"publisher","DOI":"10.1109\/70.285580"},{"key":"S0263574718000619_ref54","volume-title":"Creative Design of Mechanical Devices","author":"Yan","year":"1998"},{"key":"S0263574718000619_ref37","first-page":"257","volume-title":"Proc. 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