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  • DAAAM INTERNATIONAL SCIENTIFIC BOOK 2014 pp. 383-400 Chapter 31

    OPTIMAL SOLUTIONS FOR INVERSE STRUCTURAL MODELS OF BIMOBILE SYSTEMS

    COMANESCU, A.; COMANESCU, D.; DUGAESESCU, I., &

    UNGUREANU, L.M.

    Abstract: The inverse structure modeling of bi mobile mechanisms is based on the passive modular groups mentioned in the classical theory of mechanisms (Crossley, 1968; Pelecudi 1967). In function of the number of links and independent contours the inverse models may have a maximum number of links for their passive groups.

    Having in view the inverse models and the complex passive groups with a higher number of links and loops in the paper optimal solutions for bi mobile mechanisms is presented. Such bi mobile mechanisms applied to mechanical structures for robot arms and legs for mobile platforms ensure a higher functional precision.

    Key words: Bi-mobile mechanism, robot arm, robot leg, Baranov truss, inverse model

    Authors data: Univ.Prof. Dipl.-Ing. Dr.techn. Comanescu, A[driana]; Univ.Prof.

    Dipl.-Ing. Dr.techn. Comanescu, D[inu]; Lect.Dr.-Ing. Dugaesescu, I[leana];

    Asist.Dr.-Ing. Ungureanu, L[iviu], Mechanisms and Robots Theory Department,

    Faculty of Engineering and Management of Technological Systems, University

    Politehnica of Bucharest, Splaiul Independentei 313, 060042, Bucharest,

    Romania,adrianacomanescu@gmail.com,dinucomanescu@yahoo.com,

    ileana_d1@yahoo.com, ungureanu.liviu.marian@gmail.com This Publication has to be referred as: Comanescu, A[driana]; Comanescu, D[inu];

    Dugaesescu, I[leana] & Ungureanu, L[iviu] (2014). Optimal Solutions for Inverse

    Structural Models of Bimobile Systems, Chapter 31 in DAAAM International

    Scientific Book 2014, pp.383-400, B. Katalinic (Ed.), Published by DAAAM

    International, ISBN 978-3-901509-98-8, ISSN 1726-9687, Vienna, Austria

    DOI: 10.2507/daaam.scibook.2014.31

    mailto:adrianacomanescu@gmail.commailto:dinucomanescu@yahoo.commailto:ileana_d1@yahoo.commailto:ungureanu.liviu.marian@gmail.com

  • Comanescu, A.; Comanescu, D.; Dugaesescu, I. & Ungureanu, L.: Optimal Solutio...

    1. Introduction

    The paper, the result of many years of research is a synthesis of the past and

    present, future structural theory in the mechanisms science.

    In the last part of the 20th century the mechanisms with two degrees of mobility

    become especially usefully for various systems in robotics and other equipment

    (Angeles, 2003). In the same time two concepts direct and inverse models were

    developed (Voinea et al., 2000). For the direct model the parameters of any link and

    pair are principally expressed by those of the active pairs. For the inverse model the

    active pairs (actuators) parameters are determined relative to the effector parameters.

    The effector extremity of such mechanisms may describe any curve in the

    certain domain of the mechanism.

    The inverse structure modeling of bi mobile mechanisms is based on the passive

    modular groups mentioned in the classical theory of mechanisms (Artobolevski,

    1977; Crossley, 1968; Manolescu et all., 1972; Pelecudi 1967).

    In order to design structures for bi-mobile mechanisms the following steps are

    mentioned (Comanescu et al., 2010):

    to put into evidence the matrix of possible bases and effectors for the linkages;

    to eliminate the non-distinct solutions due to the symmetrical characteristics of the linkages;

    to verify the solutions for bases and effectors through the inverse structural model characterized by a zero instantaneous degree of mobility;

    the selection of the optimum structural-constructive solutions including a minimum number of passive modular groups;

    to place in the mechanism structure the active kinematic pairs (actuators);

    to create an optimal structural solution with a minimum number of modular groups.

    A bi-mobile planar mechanism with an optimal structure used either for a robot

    arm or for a leg of a walking robot (Kakudou et al., 2013) must contain a minimum

    number of modular passive groups for its inverse model and also a minimum number

    of modular groups for the direct model.

    2. Structural considerations

    By using the 40 linkages with three independent loops and five degrees of

    freedom (Tab. 1) the bi-mobile planar mechanisms may be obtained when somebody

    nominates the basis and the effector. All these structural solutions have nine links,

    eleven lower pairs and three independent loops.

    The mobility instantaneously becomes zero due to the placing a connection

    between the basis and the extremity of the effector and the inverse model has zero

    degree of mobility. This connection is equivalent to a lower pair with two constrains

    and a single mobility.

    http://dl.acm.org/author_page.cfm?id=81553585656&coll=DL&dl=ACM&trk=0&cfid=248503162&cftoken=90618536

  • DAAAM INTERNATIONAL SCIENTIFIC BOOK 2014 pp. 383-400 Chapter 31

    By excluding its basis the structure is composed by an even number of links,

    which determine passive modular groups [Comanescu et al., 2010].

    The planar structures with zero degree of mobility are mentioned [Manolescu et

    al., 1972) and named Baranov trusses. Any structure with zero degree of mobility has

    an odd number of links. In the literature [Artobolevski, 1977; Manolescu, 1972] there

    are mentioned the passive modular groups with 2, 4 and 6 elements.

    In the case of the previously mentioned linkages (Tab. 1) the inverse models are

    constituted by the following passive modular groups with 2+2+2+2, 2+4+2, 2+2+4,

    4+2+2, 2+6, 6+2 or 8 elements.

    L1

    1

    23

    45

    6

    78

    9

    L2

    9

    87

    6

    543

    2

    1

    L3

    9

    8 7

    6

    54

    3

    2

    1

    L4

    9

    8

    7 6

    5

    432

    1

    L5

    9

    8

    7

    6

    54

    3

    2

    1

    L6

    9 8 7

    6

    543

    2

    1

    L7

    9

    87

    6

    5

    43

    2

    1

    L8

    9

    8

    7

    6

    5

    4

    3

    21

    L9

    98

    7

    6

    5

    4

    3

    21

    L10 1

    2

    36

    5 4

    9

    7 8

    L11

    L12

    98

    7 6

    5

    432

    1

    L13

    98

    7 65

    4

    3

    2

    1

    L14

    L15

    9

    87

    6

    54

    3

    2

    1

    L16

    1

    3

    9

    8

    7

    6

    4

    5

    2

    L17

    1

    2

    3

    4

    5

    67

    8

    9

    L18

    1

    2

    3

    4

    56

    7

    8

    9

    L19

    1

    2

    3

    4

    5

    6

    7

    89

    L20

    12

    3

    4

    5

    6

    7

    8

    9

    L21

    1

    2

    3

    4

    5

    6

    7

    8

    9

    L22 1 2

    3

    45

    6

    7

    8

    9

    L23

    1

    2

    3

    45

    6

    7

    8

    9

    L24

    1

    2

    3

    4

    5

    6

    7

    8

    9

    L25

    1

    2

    3

    4

    5

    6

    7

    8

    9

    L26

    1

    2

    34

    5

    6

    78

    9

    L27

    1

    2

    3

    4

    56

    7

    8

    9

    L28

    1

    2

    3 4

    5

    678

    9

    L29

    L30 1

    2

    3

    4

    5

    6

    7

    8

    9

    9

    8

    7

    6

    5

    4

    3

    2

    1

    9

    8

    7

    6

    5

    4

    32

    1

    1

    2 3

    4

    5

    6

    7

    8 9

  • Comanescu, A.; Comanescu, D.; Dugaesescu, I. & Ungureanu, L.: Optimal Solutio...

    L31

    1

    2

    3

    4

    5

    67

    8

    9

    L32

    1

    2

    3

    4

    5

    6

    7

    8

    9

    L33

    1

    2

    3

    4

    56

    78

    9

    L34

    1

    2

    3

    4

    5

    6

    7

    8

    9

    L35

    L36

    12

    3

    4

    5

    6 7

    8

    9

    L37 1

    2

    3

    4

    5

    6

    7

    8

    9

    L38 1

    2

    3

    4

    5

    6

    7

    8

    9

    L39

    1 2 3

    4

    5

    67

    89

    L40

    123

    4

    5

    6 7

    89

    Tab. 1. Three loops planar linkages with five degrees of freedom

    The optimal solutions have only one passive modular group with 8 elements

    connected at the adopted basis. Such groups with 8 elements may be obtained from

    Baranov trusses with nine elements and four independent loops [Tab. 2] by

    eliminating a link.

    The BT1-BT5 Baranov trusses [Comanescu et al., 2010] have respectively 3, 5

    and 7 elements and 1, 2 and 3 independent loops and are eliminated in Tab. 1.

    BT 6

    1

    2

    3

    4

    5

    6

    7

    8

    9

    BT 7

    1

    2

    3

    4

    5

    67

    8

    9

    BT 8 1

    2

    3

    4

    5

    6

    7

    8

    9

    BT 9

    1

    2 3

    4

    5

    6

    7

    8 9

    BT 10

    1

    2

    3

    4

    6

    78

    5

    9

    BT 11

    1

    2

    3 4

    5

    6

    78

    9

    BT 12

    1

    2

    3

    4

    5

    6

    7

    89

    BT 13

    1

    2

    3

    4

    5

    6

    78

    9

    BT 14

    1