外文翻譯--二維多段機(jī)械系統(tǒng)基于matlab的交互式仿真程序（英文）

1、Matlab Based Interactive Simulation Program for 2D Multisegment Mechanical SystemsHenryk Josiński1,2, Adam ?witoński1,2, Karol J?drasiak1, Andrzej Polański1,2, and Konrad Wojciechowski1,21 Polish-Japanese Institute of In

2、formation Technology Aleja Legionów 2 41-902 Bytom, Poland {hjosinski,aswitonski,kjedrasiak,apolanski,kwojciechowski}@pjwstk.edu.pl 2 Silesian University of Technology Akademicka 16 44-100 Gliwice, Poland {Henryk.Jo

3、sinski;Adam.Switonski;Andrzej.Polanski; Konrad.Wojciechowski}@polsl.plAbstract. This paper presents principles of designing multisegment me- chanical system. Represented is a model of a single segment, its extension in f

4、orm of a couple of segments and the final construction – a fragmentary and simplified silhouette of a human form named the biped. This paper describes procedure of construction of the biped’s digital model using Matlab p

5、ackage. It also discusses test run of a single experiment and algorithm of the calculations realized in the single step of integration.1 IntroductionScientists create physical and mathematical models of movement of a who

6、le human form or its specified parts. Mathematical models enable creation of digi- tal models to conduct computer simulation. Model testing makes it possible to analyse decomposition of forces and torques in a non-invasi

7、ve way. The purpose of this research was to build a simple multisegment movement model in order to determine the principles of adding the successive segments and how to avoid their break-up. This is how the silhouette na

8、med biped was created. Its digital model created using Matlab package should enable to carry out simulation of the biped’s movement. Literature related to this subject is extensive. Analysis of contents of a move- ment m

9、odel was included in [9]. The dynamics of planar human body motion, solved with a non-iterative matrix formulation was presented in [1]. Worth men- tioning is also item [3] of the bibliography where Brubaker et al propos

10、ed a model based on the Anthropomorphic Walker [5, 6], a physics-based planar model with two straight legs, a single torsional spring and an impulsive collision model. The Anthropomorphic Walker is simple, as it only exh

11、ibits human-like gaits on level ground. Brubaker et al [2] introduced also the Kneed Walker – a complex model of bipedal locomotion based on biomechanical characterizations of human walking [7]. It has a torso and two le

12、gs with knees and ankles. It is capable of exhibiting a wide range of plausible gait styles. A mathematical model of the swing phase of walking was presented in [8].Matlab Based Interactive Simulation Program 3Up to date

13、 segment’s ends’ components are calculated using simple trigono- metric equations:x1 = X + l sin ?2 y1 = Y ? l cos ?2 (4)x2 = X ? l sin ?2 y2 = Y + l cos ?2 (5)Differentiation allows to calculate vertical and horizontal

14、components of seg- ment’s ends’ velocity:˙ x1 = ˙ X + ˙ ?l cos ?2 ˙ y1 = ˙ Y + ˙ ?l sin ?2 (6)˙ x2 = ˙ X ? ˙ ?l cos ?2 ˙ y2 = ˙ Y ? ˙ ?l sin ?2 (7)Successive differentiation leads to formulae describing segment’s ends’ a

15、ccel- eration:¨ x1 = ¨ X + ¨ ?l cos ?2 ? ˙ ?2 l sin ?2 ¨ y1 = ¨ Y + ¨ ?l sin ?2 + ˙ ?2 l cos ?2 (8)¨ x2 = ¨ X ? ¨ ?l cos ?2 + ˙ ?2 l sin ?2 ¨ y2 = ¨ Y ? ¨ ?l si

16、n ?2 ? ˙ ?2 l cos ?2 (9)Equations describing state of the segment allow to formulate general rela- tionship between accelerations of the segment’s ends and external influences – forces and a control torque M:?? ? ?¨

17、 x1 ¨ y1 ¨ x2 ¨ y2?? ? ? = Mcoef?? ? ? ? ? ? ?F1x F1y F2x F2y M 1?? ? ? ? ? ? ?(10)Symbol Mcoef represents coefficients’ matrix determined by the formulas (8), (9) allowing for equations (1), (2), (3).3 Mo

18、del of Couple of Segments MovementThe case of 2 joined segments requires doubling of the state variables’ set applied for the case of a single segment. Decomposition of forces and torques is shown on Fig. 2 (index U deno