Blajer, WojciechWojciechBlajerSeifried, RobertRobertSeifriedKołodziejczyk, KrzysztofKrzysztofKołodziejczyk2021-11-112021-11-112015-02-01Archive of Applied Mechanics 85 (9/10): 1191-1207 (2015-09-13)http://hdl.handle.net/11420/10882The paper deals with underactuated mechanical systems, featured by less control inputs m than degrees of freedom f, m < f, subject to m servo-constraints (specified in time outputs) on the system. The arising servo-constraint problem (inverse dynamics analysis) is discussed with an emphasis on the way the servo-constraints are realized, varying from orthogonal to tangential, and a geometrical illustration of the different realization types is provided. Depending on the way the servo-constraints are realized, the governing equations are formulated either as ordinary differential equations (ODEs) or differential-algebraic equations (DAEs), and some computational issues for the ODEs and DAEs are discussed. The existence or non-existence of an explicit solution to the governing equations is further discussed, related to so-called differentially flat problems (without internal dynamics) and non-flat problems (with internal dynamics). It is shown that in case of non-flat problems with orthogonal realization of servo-constraints, stability of the internal dynamics must be assured. Simple case studies are reported to illustrate the proposed formulations and methodologies.en1432-068120159/1011911207Springerhttps://creativecommons.org/licenses/by/4.0/Inverse dynamicsServo-constraintsUnderactuated systemsTechnikJournal Article10.15480/882.388910.1007/s00419-014-0959-210.15480/882.3889Other