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## Modeling of Elastically Coupled Bodies: Part I-General Theory and Geometric Potential Function Method

### Citations

38 |
A classification of robot compliance”.
- Patterson, Lipkin
- 1990
(Show Context)
Citation Context ...ons are derived in a form suitable for automatic computation. 1 Introduction Modeling, analysis and simulation of flexible, spatial multibody systems is a challenging problem of considerable practical importance. There is significant literature looking at the geometry of compliance. Dimentberg (1965) looks at the geometry of a single rigid body supported by a system of ideal linear springs. Loncaric (1987, 1988) showed that stiffness and compliance matrices could be parameterized in an intuitive geometrical way. Griffis and Duffy (1991) looked at the geometry of compliance using screw theory. Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined using different implicitly defined affine connections. Huang and Schimmels (1997) look at the realizability of spatial stiffnesses using parallel connections of "simple springs." 2 Problem Statement Shown in Fig. 1 is a pair of rigid bodies connected by an elastic body. The elastic body need not be an axisymmetric beam. Pan... |

37 | Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms,"
- Howell, Midha, et al.
- 1996
(Show Context)
Citation Context ... ~ " /a(o) = ~fb{a) = 0 r;;(„) = -fS(„, « 2 a s {GM) f^c) = -flc, ^ 2 as {GM) fafr)= - fb f r )«2as {G,6pl) (31) (32) (33) 'fV « K '8pV 691 = K, Kc _K, K„_ -6pV _6ei_ In general it is true that C = Aw + vPA' if and only if i; = (tr (A)/ - A')w. It follows that (34) This shows that matrices K,, K„, and Kc determine the stiffness of the system at H^ = Hb as claimed. It is also true in equilibrium that wl « KSn, wl « KSTl, and wt « KSTl It is not claimed that the results are valid for large displacements. There is much solid mechanics literature regarding large deformations of elastic materials. Howell and Midha (1994) look at large deflections of planar, compliant mechanisms. 6 Summary The goal of this research was to define compliance families that (1) were parameterized in an intuitive, geometrical way, (2) had desirable geometric and other properties, and (3) had constitutive equations that could be computed automatically for numerical simulation. The parameterization used was derived from that of Loncaric. Parameters were calculated for an elastic beam. The "desirable geometric and other properties" were sufficient diversity, parsimony, frame-indifference and port-indifference. A novel compliance famil... |

31 |
Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement,”
- Griffis, Duffy
- 1991
(Show Context)
Citation Context ...ions. The configuration-dependent wrenches corresponding to these potential functions are derived in a form suitable for automatic computation. 1 Introduction Modeling, analysis and simulation of flexible, spatial multibody systems is a challenging problem of considerable practical importance. There is significant literature looking at the geometry of compliance. Dimentberg (1965) looks at the geometry of a single rigid body supported by a system of ideal linear springs. Loncaric (1987, 1988) showed that stiffness and compliance matrices could be parameterized in an intuitive geometrical way. Griffis and Duffy (1991) looked at the geometry of compliance using screw theory. Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined using different implicitly defined affine connections. Huang and Schimmels (1997) look at the realizability of spatial stiffnesses using parallel connections of "simple springs." 2 Problem Statement Shown in Fig. 1 is a pair of rigid bodies ... |

8 | Affine Connections for the Cartesian Stiffness Matrix,"
- Zefran, Kumar
- 1997
(Show Context)
Citation Context ...lexible, spatial multibody systems is a challenging problem of considerable practical importance. There is significant literature looking at the geometry of compliance. Dimentberg (1965) looks at the geometry of a single rigid body supported by a system of ideal linear springs. Loncaric (1987, 1988) showed that stiffness and compliance matrices could be parameterized in an intuitive geometrical way. Griffis and Duffy (1991) looked at the geometry of compliance using screw theory. Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined using different implicitly defined affine connections. Huang and Schimmels (1997) look at the realizability of spatial stiffnesses using parallel connections of "simple springs." 2 Problem Statement Shown in Fig. 1 is a pair of rigid bodies connected by an elastic body. The elastic body need not be an axisymmetric beam. Panel (A) depicts the undeformed system in static equilibrium. Panel (b) depicts the deformed system. The configura... |

6 | On the 6 X 6 Stiffness Matrix for Three Dimensional Motions,"
- Howard, Zefran, et al.
- 1995
(Show Context)
Citation Context ...ystems is a challenging problem of considerable practical importance. There is significant literature looking at the geometry of compliance. Dimentberg (1965) looks at the geometry of a single rigid body supported by a system of ideal linear springs. Loncaric (1987, 1988) showed that stiffness and compliance matrices could be parameterized in an intuitive geometrical way. Griffis and Duffy (1991) looked at the geometry of compliance using screw theory. Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined using different implicitly defined affine connections. Huang and Schimmels (1997) look at the realizability of spatial stiffnesses using parallel connections of "simple springs." 2 Problem Statement Shown in Fig. 1 is a pair of rigid bodies connected by an elastic body. The elastic body need not be an axisymmetric beam. Panel (A) depicts the undeformed system in static equilibrium. Panel (b) depicts the deformed system. The configuration of a rigid body can ... |

2 |
Structure of Robot Comphance,"
- Patterson, Lipkin
- 1993
(Show Context)
Citation Context ...ons are derived in a form suitable for automatic computation. 1 Introduction Modeling, analysis and simulation of flexible, spatial multibody systems is a challenging problem of considerable practical importance. There is significant literature looking at the geometry of compliance. Dimentberg (1965) looks at the geometry of a single rigid body supported by a system of ideal linear springs. Loncaric (1987, 1988) showed that stiffness and compliance matrices could be parameterized in an intuitive geometrical way. Griffis and Duffy (1991) looked at the geometry of compliance using screw theory. Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined using different implicitly defined affine connections. Huang and Schimmels (1997) look at the realizability of spatial stiffnesses using parallel connections of "simple springs." 2 Problem Statement Shown in Fig. 1 is a pair of rigid bodies connected by an elastic body. The elastic body need not be an axisymmetric beam. Pan... |

1 |
The Screw Calculus and Its Applicalions
- Dimentberg
- 1965
(Show Context)
Citation Context ...rable properties of compliance families are defined (sufficient diversity, parsimony, frame-indifference, and port-indifference). A novel compliance family witii the desired properties is defined using geometric potential energy functions. The configuration-dependent wrenches corresponding to these potential functions are derived in a form suitable for automatic computation. 1 Introduction Modeling, analysis and simulation of flexible, spatial multibody systems is a challenging problem of considerable practical importance. There is significant literature looking at the geometry of compliance. Dimentberg (1965) looks at the geometry of a single rigid body supported by a system of ideal linear springs. Loncaric (1987, 1988) showed that stiffness and compliance matrices could be parameterized in an intuitive geometrical way. Griffis and Duffy (1991) looked at the geometry of compliance using screw theory. Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined ... |

1 |
The Realizable Space of Spatial Stiffnesses Achieved With a Parallel Connection of Simple Springs,"
- Huang, Schimmels
- 1997
(Show Context)
Citation Context ... by a system of ideal linear springs. Loncaric (1987, 1988) showed that stiffness and compliance matrices could be parameterized in an intuitive geometrical way. Griffis and Duffy (1991) looked at the geometry of compliance using screw theory. Patterson and Lipkin (1993b, 1993a) went on to classify compliance in terms of screw eigenvalues and eigenvectors. Zefran and Kumar (1997) and Howard et al. (1995) have also looked at the geometry of compliance, explaining for example differences in the structure of the stiffness matrix when defined using different implicitly defined affine connections. Huang and Schimmels (1997) look at the realizability of spatial stiffnesses using parallel connections of "simple springs." 2 Problem Statement Shown in Fig. 1 is a pair of rigid bodies connected by an elastic body. The elastic body need not be an axisymmetric beam. Panel (A) depicts the undeformed system in static equilibrium. Panel (b) depicts the deformed system. The configuration of a rigid body can be represented by a frame,-which in turn can be identified with a homogeneous matrix H R p 0' 1 (1) where R = [e, e^ 63] is an orthonormal matrix and p is a linear displacement vector. Six such frames are shown in Fig. ... |

1 | Normal Forms of Stiffness and Compliance Matrices," - Lon£aric - 1987 |

1 | On Statics of Elastic Systems and Networks of Rigid Bodies," - Lonbaric - 1988 |