Haug, E. J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....set of parametric analyses and, in a short time, even with a complete system optimization. The technology of multi body is not mature yet, with particular regard to the aeronautical and specifically the aeroservoelastic field. Current commercial general purpose multi body analysis codes, e.g. DADS [8], MECANO [3] ADAMS and others [20] still pose some limitations to the modeling of rotorcrafts, mainly due to insufficient aerodynamics, insufficient description of flexible bodies, and in some cases to limitations in the integration algorithms when applied to large finite rotations of the order ....

Haug, E. J., Computer Aided Kinematics and Dynamics of Mechanical Systems. Vol. 1: Basic Methods Boston, Allyn and Bacon, 1989

....of index 2 and when a(t, y) y we obtain Hessenberg DAEs of index 2 [2, 5, 7] The DAEs (1. 1) include the formulation of mechanical systems with mixed holonomic, nonholonomic, scleronomic, and rheonomic constraints provided holonomic constraints are di#erentiated once explicitly with respect to t [8, 16, 17, 18]. The algebraic variable z corresponds to # Received February 2002. Revised August 2002. Communicated by Christian Lubich. This material is based upon work supported by the National Science Foundation under Grant No. 9983708. Lagrange multipliers when the DAEs can be derived from a variational ....

....variable z corresponds to # Received February 2002. Revised August 2002. Communicated by Christian Lubich. This material is based upon work supported by the National Science Foundation under Grant No. 9983708. Lagrange multipliers when the DAEs can be derived from a variational principle [8, 16]. Solutions to these DAEs (1.1) can be approximated numerically by applying a class of super partitioned additive Runge Kutta (SPARK) methods, such as the combination of Lobatto IIIA B C C # D methods [10] SPARK methods can take advantage of splitting the di#erential equations into di#erent ....

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E. J. Haug, Computer aided kinematics and dynamics of mechanical systems. Volume I: Basic methods, Allyn and Bacon, Boston, USA, 1989.

.... of possibly stiff and implicit differential algebraic equations (DAEs) is considered, including Hessenberg DAEs of index 1, 2, and 3 [1,5,6,8,9] These equations encompass the formulation of mechanical systems with mixed constraints of holonomic, nonholonomic, scleronomic, and rheonomic types [7,16,17]. Solutions to these DAEs can be approximated numerically by applying a class of super partitioned additive Runge Kutta (SPARK) methods, such as the combination of Lobatto IIIA B C C # D methods [9] SPARK methods can take advantage of splitting the differential equations into different terms ....

....(1c) m(t, y, z, u, # ) 0, 1d) 0, 1e) which may present some stiffness. These equations encompass Hessenberg DAEs of index 1, 2, and 3 [1,5,6,8,9] They also include the formulation of mechanical systems with mixed constraints of holonomic, nonholonomic, scleronomic, and rheonomic types [7,13,16,17]. In mechanics the quantities q,v,p represent respectively gener alized coordinates, generalized velocities, and generalized momenta. The right hand side f of (1b) contains generalized forces acting on the system and (1c) describes the dynamics of external variables u. The algebraic variables # ....

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E.J. Haug, Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol. I: Basic Methods (Allyn and Bacon, Boston, USA, 1989).

....even the most complex models are likely to require a turnaround time that is compatible with an extensive set of parametric analyses and, within not so long a time, even with a complete system optimisation. Unfortunately, current commercial general purpose multi body analysis codes, e.g. DADS [9], MECANO [3] ADAMS and others [25] still pose some limitations to the modelling of rotorcrafts, mainly due to insufficient aerodynamics, insufficient description of flexible bodies, and in some cases to limitations in the integration algorithms when applied to large finite rotations of the order ....

Haug, E. J., Computer Aided Kinematics and Dynamics of Mechanical Systems. Vol. 1: Basic Methods Boston, Allyn and Bacon, 1989

....we use a point plane constraint for each vertex of the base. For completeness, assume that the system has, in addition to contact constraints, L joint type constraints defined by the map Theta(q) taking the configuration space to R L . For details concerning joint constraints see, for example, [4]. With these two maps, we can formulate the contact problem: Problem Given the positions q and velocities q of a set of bodies, find the accelerations that define a motion consistent with the following equality and inequality constraints. Phi(q) 0 (2.4) Theta(q) 0 (2.5) It is known [4] ....

....[4] With these two maps, we can formulate the contact problem: Problem Given the positions q and velocities q of a set of bodies, find the accelerations that define a motion consistent with the following equality and inequality constraints. Phi(q) 0 (2.4) Theta(q) 0 (2. 5) It is known [4] that for frictionless cases the direction of the constraint force is perpendicular to the manifold defining the constraint surface. Thus the forces due to active contact constraints are of the type Phi q (q) where is the vector of the contact forces. Similarly Theta q (q) is the ....

E.J.Haug. Computer aided kinematics and dynamics of mechanical systems. Allyn and Bacon, 1989.

....[2] at this time no code seems to exploit both the structure of the optimization matrix and the sparsity in a satisfying manner. The paper is organized as follows: first a brief introduction to the issue of formulating a multibody dynamics problem using the fully cartesian approach as presented in [9] is provided. Next we discuss the way in which the structure of the problem can be taken advantage of; we show that it is more efficient to first solve a reduced system for the Lagrange multipliers and then determine the accelerations by solving diagonal or almost diagonal systems of equations. A ....

....numbering is stated. It will turn out that the optimal numbering of the vertices of the associated graph has an immediate corespondent in the joint numbering of the mechanical system. Then it will be shown that a widely used alternative for computing the accelerations and Lagrange multipliers [4] [9], can be easily modified in order to take advantage of the new algorithm. The discussion is exemplified by means of a seven body mechanism and an open chain of simple rigid pendulums. The results of some numerical experiments aimed to showing the effectiveness of the proposed strategy are ....

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E. J. Haug, Computer--Aided Kinematics and Dynamics of Mechanical Systems, Volume I: Basic Methods, Allyn and Bacon, 1989

....of coordinates appearing in the final equations can be controlled. As an example, the equations can be generated in joint coordinates [14] by selecting as many joints as possible into the tree (hereafter called a joint tree ) Alternatively, the equations will be in terms of absolute coordinates [15] if all bodies are selected into the tree. In either case, the elastic coordinates q f will also appear in the equations of motion if there are flexible bodies in the system. A mix of bodies, joints, or even force and torque elements, can be selected into the tree to obtain a hybrid set of branch ....

....numerical algorithms for differential algebraic equations [13] Numerical methods must also be used to handle lockup or bifurcation configurations, for which the Jacobian matrices f Phig q and f Phig q d become singular when evaluated. There are several numerical methods for singularity handling [14, 15] that can be applied to our symbolic equations. Although a detailed discussion is beyond the scope of this paper, we speculate that these methods might by facilitated by our formulation, which could re generate system equations in a new set of coordinates whenever a singular configuration is ....

E.J. Haug, Computer-Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, 1989.

.... elastic rotation is simply the elastic rotation matrix of the section on which the point is located, that is, R 2 = R i f (26) The terminal equation at the angular velocity level is 2 = fe g T R i 1 8 : f1 f2 f3 9 = 27) where f1 ; f2 and f3 are found [18] with dR i f dt R i f T = 2 6 4 0 Gamma f3 f2 f3 0 Gamma f1 Gamma f2 f1 0 3 7 5 4 = f (28) which is the skew symmetric matrix of the angular velocity of the sectional frame relative to the body frame and is expressed in the body frame as well. The terminal equation at ....

E.J. Haug, Computer-aided kinematics and dynamics of mechanical systems, Allyn and Bacon, 1989.

....are cut in the topology analysis process are replaced by a set of constraint equations. Constraints between solid bodies are often characterized by conditions of orthogonality or parallelism of pairs of such vectors. The original work for deriving a library of possible constraints was presented by Haug (1989), and was implemented into a commercial dynamics analysis software called DADS (Cadsi 1995) The study of the derivatives of the mechanism s performance with respect to a design variable is called design sensitivity analysis (Tak and Kim 1990) The work by Haug and colleagues is further expanded ....

....the automation of mechanical design. It can also be used to study different scenarios of a particular design. The ultimate goal is to extend this work to include the propagation of dynamics in mechanisms and machines. 2 Cut Joint Constraint Formulation Cut joint methods (Wittenburg 1977 and Haug 1989) are used to handle closed loop systems to form a spanning tree that has no closed loops. Joints that are cut in the topology analysis process are replaced by a set of constraint equations. Partial derivatives of basic constraints with respect to design variables are derived in Cartesian ....

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Haug, E. J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems Vol I Allyn & Bacon.

....by the array of generalized velocities q = q 1 ; q n ] T . Given the quantities q and q, the position and velocity of each body in the system is uniquely determined. There is a multitude of ways in which the set of generalized coordinates and velocities can be selected [5, 9, 6]. The generalized coordinates used in this paper are Cartesian coordinates for position, and Euler parameters for orientation of body centroidal reference frames. Thus, for each body i the position of the body is described by the vector p i = x i ; y i ; z i ] T , while the orientation is given ....

....in this paper are Cartesian coordinates for position, and Euler parameters for orientation of body centroidal reference frames. Thus, for each body i the position of the body is described by the vector p i = x i ; y i ; z i ] T , while the orientation is given by the array of Euler parameters [9], e i = e i0 ; e i1 ; e i2 ; e i3 ] T . Consequently, for a mechanical system containing nb bodies, q = p T 1 e T 1 : p T nb e T nb T 2 R 7nb : 1) When compared with the alternative of using a set of relative generalized coordinates, the coordinates considered are ....

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E. J. Haug. Computer-Aided Kinematics and Dynamics of Mechanical Systems. Allyn and Bacon, Boston, London, Sydney, Toronto, 1989.

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Haug, E. J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon.

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Haug, E. J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon.

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Haug, E., Computer-Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon (1989).

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E. J. Haug, Computer-Aided Kinematics and Dynamics of Mechanical Systems, Basic Method. Boston, MA: Allyn and Bacon, 1989.

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E. J. Haug, Computer-aided kinematics and dynamics of mechanical systems, vol. I, Allyn and Bacon, 1989, pp 48#104.

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E.J.Haug. Computer aided kinematics and dynamics of mechanical systems. Allyn and Bacon, 1989.

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Haug EJ (1989) Computer-Aided Kinematics and Dynamics of Mechanical SystemsBasic Methods. Allyn and Bacon, Boston

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Haug,E.J.,Computer Aided Kinematics and Dynamics of Mechanical Systems,Allyn and Bacon, Boston, 1989.

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Haug, E.J., Computer-Aided Kinematics and Dynamics of Mechanical Systems-Basic Methods, Allyn and Bacon, 1989.

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Haug, E.J.: ComputerAided Kinematics and Dynamics of Mechanical Systems.Allyn and Bacon, Boston, 1989

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Haug, E. J., Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, 1989.

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Haug, E. J., Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, 1989.

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Haug, E. J., Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, 1989.

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E. J. Haug, Computer Aided Kinematics and Dynamics of Mechanical Systems. Vol. I: Basic Methods, Allyn and Bacon, Boston, MA, 1989.

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E. Haug (1989) Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol. I: Basic Methods, All n and Bacon, Pub.

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