Janusz Frączek

For rigid multibody systems with redundant constraints, mathematical modeling and physical interpretation of the obtained results are impeded due to the nonuniqueness of the calculated reactions, which—in the case of load-dependent joint friction—may additionally lead to unrealistic simulated motion. It makes the uniqueness analysis crucial for assessing the fidelity of the results. The developed methods so far for the uniqueness examination—based on the modified mobility equation, the constraint matrix, or the free-body diagram—are not well suited for multibody systems described by relative coordinates. The novel method discussed in this paper breaks this limitation. The proposed approach is based on the divide-and-conquer algorithm (DCA)—a low-order recursive method for dynamic simulations of complex multibody systems. The devised method may be used for checking the joint-reaction uniqueness of holonomic systems with ideal constraints that fulfill some additional assumptions. The reaction-uniqueness analysis is performed when the main pass of the DCA is completed. An eight-step algorithm is proposed. In the case of the single-joint connections, it is sufficient to study the appropriate equations of motion. However, if the multijoint connection is present, then one of the numerical methods—known from the constraint-matrix-based or the free-body-diagram-based approach—has to be used, namely the rank-comparison, QR-decomposition, SVD, or nullspace methods; all of these approaches are discussed. To illustrate the devised method, a spatial parallelogram mechanism with a triple pendulum is analyzed.

This paper presents a joint–coordinate adjoint method for optimal control of multi-rigid-body systems. Initially formulated as a set of differential-algebraic equations, the adjoint system is brought into a minimal form by projecting the original expressions into the joint’s motion and constraint force subspaces. Consequently, cumbersome partial derivatives corresponding to joint-space equations of motion are avoided, and the approach is algorithmically more straightforward. The analogies between the formulation of Hamilton’s equations of motion in a mixed redundant-joint set of coordinates and the necessary conditions arising from the minimization of the cost functional are demonstrated in the text. The observed parallels directly lead to the definition of a joint set of adjoint variables. Through numerical studies, the performance of the proposed approach is investigated for optimal control of a double pendulum on a cart. The results demonstrate a successful application of the joint-coordinate adjoint method. The outcome can be easily generalized to optimal control of more complex systems.

Summary: The design of multibody systems involves high fidelity and reliable techniques and formulations that should help the analyst to make reasonable decisions. Given that constrained equations of motion for the simplest of multibody systems are highly nonlinear, determining the sensitivity terms is a computationally intensive and complex process that requires the application of special procedures. In this article, two novel Hamiltonian‐based approaches are presented for efficient sensitivity analysis of general multibody systems. The developed direct differentiation and the adjoint methods are based on constrained Hamilton's canonical equations of motion. This formulation provides solutions, which are more stable as compared to the results of direct integration of equations of motion expressed in terms of accelerations due to a reduced differential index of the underlying system of differential‐algebraic equations and explicit constraint imposition at the velocity level.The proposed Hamiltonian based methods are both capable of calculating the sensitivity derivatives and keeping the growth of constraint violation errors at a reasonable rate. The Hamiltonian‐based procedures derived herein appear to be good alternatives to existing methods for sensitivity analysis of general multibody systems.

Objective: to quantitatively assess disturbances of sweet, sour and salty and bitter tastes in a group of young, asymptomatic or oligosymptomatic COVID-19 patients; establish a reliable, sensitive and specific test that can diagnose COVID-19 on the basis of taste disorders and publish the results according to STARD 2015 statement (Standards for Reporting Diagnostic Accuracy). Design: case-control study Setting: isolated rooms in the Central Clinical Hospital of the Ministry of the Interior and Administration in Warsaw (which had been transformed into an infectious hospital) and a dormitory in one of Warsaw universities. Participants: 52 SARS-CoV-2 positive (51 men, mean age 21.7 years) and 36 negative students (34 men, mean age 20.8 years). Main outcome measures: a gustatory function assessment (sweet, salty, sour and bitter taste), with flavour concentrations established previously in healthy subjects was conducted for all subjects. Each participant received one tasteless reference and nine flavour tablets with sucrose concentrations of 40, 80 and 106.4 mg/ml; NaCl at 13.5, 17 and 27 mg/ml; ascorbic acid at 6.25 and 12.5 mg/ml and grapefruit extract at 40 mg/ml. Results: the only taste that was impaired significantly more frequently in COVID-19 patients was the sweet taste at the lowest flavour concentration (40 mg/ml, p = 0.002). Different screening and diagnostic models were constructed using the examined variables. The highest accuracy screening test consisted of the positive result of a three-question questionnaire (self-reported loss of taste, self-reported loss of smell, or fever within the last month (positive if at least one present) and/or ageusia of sweet taste at a sucrose concentration of 40 mg/ml. The sensitivity of the model was 94% with a specificity of 55%. The highest accuracy diagnostic test consisted of ageusia of sweet taste at a sucrose concentration of 106.4 mg/ml or/and ageusia of salty taste at an NaCl concentration of 13.5 or 17 mg/ml. The specificity of the test was found to be 100%, and the sensitivity was 34%. Conclusion: as the most effective way of controlling the present pandemic involves testing the wider population for symptomatic, oligosymptomatic and asymptomatic carriers of SARSCoV-2 and isolating or hospitalising infected subjects, in the present study, an inexpensive, simple, fast and sensitive (94%) screening test that can be used for such a purpose is proposed. In addition, a specific (100%) diagnostic test that could be used to refer patients to quarantine in the case of limited availability of genetic or serological tests is proposed.

Parallel computers are becoming more available. The natural way to improve computational efficiency of multibody simulations seems to be parallel processing. Within this work we are trying to estimate the efficiency of parallel computations performed using one of the commercial multibody solver. First, the short theoretical outline is presented to give the overview of modeling issues in multibody dynamics. Next, the experimental part is demonstrated. The series of dynamics analyses are carried out. The test mechanisms with variable number of bodies are used to gather the performance results of the solver. The obtained data allow for estimating the number of bodies which are sufficient to gain benefits from parallel computing as well as their level. The parallel processing profits are taken into account in the case of contact forces present in the system. The performance benefits are indicated, when the multilink belt chain is simulated, in which contact forces are included in the model.