Introduction to Polynomial Invariants of Screw Systems

Screw systems describe the infinitesimal motion of multi–degree-of-freedom rigid bodies, such as end-effectors of robot manipulators. While there exists an exhaustive classification of screw systems, it is based largely on geometrical considerations rather than algebraic ones. Knowledge of the polynomial invariants of the adjoint action of the Euclidean group induced on the Grassmannians of screw systems would provide new insight to the classification, along with a reliable identification procedure. However many standard results of invariant theory break down because the Euclidean group is not reductive. We describe three possible approaches to a full listing of polynomial invariants for 2–screw systems. Two use the fact that in its adjoint action, the compact subgroup SO(3) acts as a direct sum of two copies of its standard action on R3. The Molien–Weyl Theorem then provides information on the primary and secondary invariants for this action and specific invariants are calculated by analyzing the decomposition of the alternating 2–tensors. The resulting polynomials can be filtered to find those that are SE(3) invariants and invariants for screw systems are determined by considering the impact of the Plücker relations. A related approach is to calculate directly the decomposition of the symmetric products of alternating tensors. Finally, these approaches are compared with the listing of invariants by Selig based on the existence of two invariant quadratic forms for the adjoint action

On the regularity of the inverse jacobian of parallel robots

Checking the regularity of the inverse jacobian matrix of a parallel robot is an essential element for the safe use of this type of mechanism. Ideally such check should be made for all poses of the useful workspace of the robot or for any pose along a given trajectory and should take into account the uncertainties in the robot modeling and control. We propose various methods that facilitate this check. We exhibit especially a sufficient condition for the regularity that is directly related to the extreme poses that can be reached by the robot

On the regularity of the inverse jacobian of parallel robots

Checking the regularity of the inverse jacobian matrix of a parallel robot is an essential element for the safe use of this type of mechanism. Ideally such check should be made for all poses of the useful workspace of the robot or for any pose along a given trajectory and should take into account the uncertainties in the robot modeling and control. We propose various methods that facilitate this check. We exhibit especially a sufficient condition for the regularity that is directly related to the extreme poses that can be reached by the robot

Does managed care make a difference? Physicians' length of stay decisions under managed and non-managed care

BACKGROUND: In this study we examined the influence of type of insurance and the influence of managed care in particular, on the length of stay decisions physicians make and on variation in medical practice. METHODS: We studied lengths of stay for comparable patients who are insured under managed or non-managed care plans. Seven Diagnosis Related Groups were chosen, two medical (COPD and CHF), one surgical (hip replacement) and four obstetrical (hysterectomy with and without complications and Cesarean section with and without complications). The 1999, 2000 and 2001 – data from hospitals in New York State were used and analyzed with multilevel analysis. RESULTS: Average length of stay does not differ between managed and non-managed care patients. Less variation was found for managed care patients. In both groups, the variation was smaller for DRGs that are easy to standardize than for other DRGs. CONCLUSION: Type of insurance does not affect length of stay. An explanation might be that hospitals have a general policy concerning length of stay, independent of the type of insurance of the patient