管道相貫線自動(dòng)切割機(jī)器人支撐定位系統(tǒng)設(shè)計(jì)含proe三維及17張CAD圖,管道,相貫線,自動(dòng),切割,機(jī)器人,支撐,支持,定位,系統(tǒng),設(shè)計(jì),proe,三維,17,cad Available online at www.sciencedirect.com Mechanism and Machine Theory 43 (2008) 984–995  Mechanism and Machine Theory www.elsevier.com/locate/mechmt A type synthesis method for hybrid robot structures Alexandre Campos *, Christoph Budde, Ju¨ rgen Hesselbach Institute of Machine Tools and Production Technology, Technical University of Braunschweig, Langer Kamp 19 B, D-38106 Braunschweig, Germany Received 11 May 2006; received in revised form 30 April 2007; accepted 11 July 2007 Available online 24 October 2007 Abstract In this paper a new methodology to synthesize hybrid robots as a whole structure is presented. The method is based on Assur groups as the simplest basic blocks to build kinematic chains. Criterions like symmetry and low inertia are consid- ered in the design process. The method results in hybrid robots whose structures are as simple as possible. The closed chains of some of them are known parallel structures, however one of them is a new hybrid structure. 2007 Published by Elsevier Ltd. Keywords: Hybrid robot; Synthesis method; Assur groups 1. Introduction Hybrid structures combine the advantages of parallel and serial chains, e.g. stiffness and manipulability [1– 6]. Most robots designed are either built up of serial or in-parallel connected kinematic chains. Serial robots consist of a series of active joints connecting the base to the end effector and feature large workspaces and high dexterity but they suffer from lack of stiffness and from relatively large positioning errors due to their canti- lever type of kinematic arrangement. On the other hand, parallel manipulators consist of a set of parallel legs each with active and passive joints required to maintain the system mobility and controllability. They connect the base to the moving platform resulting in structures able to achieve high stiffness and high force-to-weight ratio. However, parallel manipulators are known for a restricted workspace and low dexterity. Aiming to merge the advantages of serial and parallel robots, the basic principle of hybrid kinematic struc tures is to divide the task of manipulation [1]. This task is divided into a position task (position mechanism) and an orientation task (orientation mechanism), respectively. The position mechanism controls the position whereas the orientation mechanism manipulates the orientation of the end effector. Then, these mechanisms may be connected in series, called conventional hybrid structure, or in parallel, i.e. cooperative structure [1,8]. Additionally, the serial combinations of serial and parallel structures can be sub-divided into [3]: parallel– parallel type [6], parallel–serial type [7] and serial–serial type, i.e. a conventional serial manipulator. In this * Corresponding author. E-mail addresses: a.campos@iwf.ing.tu-bs.de (A. Campos), ch.budde@tu-bs.de (C. Budde). 0094-114X/$ - see front matter 2007 Published by Elsevier Ltd. doi:10.1016/j.mechmachtheory.2007.07.006 A. Campos et al. / Mechanism and Machine Theory 43 (2008) 984–995 985 work, we focus on the conventional hybrid structure of parallel–serial type, named hybrid structure for short. Therefore, by using hybrid structures it is intended to retain the merits of serial structures, i.e. large workspace and high dexterity, and parallel structures, i.e. high stiffness and high force-to-weight ratio, while their disad- vantages are minimized. Analysis and modeling have been the main research field in hybrid robots [1,3,9–12], additionally some researches have dealt with the design of hybrid robots [4–6]. In spite of the cited advantages of hybrid robots, there is no systematic method to design or synthesize hybrid robots as a whole structure instead of a separated synthesis for the parallel and the serial structure. This paper proposes a synthesis method for hybrid robots as a whole, built up of sets of Assur groups. It is based on a method for finger synthesis which guarantees the simplest structures, i.e. the least number of bodies and one degree of freedom (dof) joints [13], however the presented method does not use computer algorithms which may result in chain isomorphisms. Section 2 presents a brief introduction to Assur groups, then the hybrid kinematic design and some require- ments for a suitable hybrid robot are introduced. To illustrate the method, all simplest possible chains for six degrees of freedom (DOF) of the end effector with 3, 4 and 5 fixed drives are presented. Based on the method a symmetrical hybrid robot is found whose closed structure topology is new according to the knowledge of the authors. Finally, the joints are allocated into the hybrid chain and for the new robot an embodiment is pro- posed based on legs for fully isotropic translational parallel robots [14]. 2. Assur groups One of the main approaches employed in the literature for carrying out the structural synthesis of kinematic chains is to build up desired chains by addition of links to simpler chains with fewer links [15]. Assur (1952) introduced kinematic chains named Assur groups, that are open subsets of links, which can be added to a kine- matic chain without affecting the mobility of the chain [16,17]. Additionally, when the group is connected to a link through all of its free joints, shown as black joints in Fig. 1, it becomes a structure with zero degrees of freedom. Assur proposes that complex chains may be formed from the addition of Assur groups to chains with fewer links because this addition does not alter the degree of freedom of the chain. Manolescu uses the Assur groups to build kinematic chains with 8-, 9- and 10-links [17–19]. Tischler et al. implement a systematic method to generate Assur groups from minimal kinematic chains for several screw systems and apply it to the structural synthesis of multi-tipped fingers of a robotic hand [20]. Jinkui et al. apply Assur groups to investigate chains with multiple joints [21]. Yannou et al. use Assur groups as modular components for the design of platforms for planar mechanisms [22]. Regarding that an Assur group may be built up by sequential addition of Assur groups, Tischler [13] intro- duced the concept of Minimal Assur groups, i.e. Assur groups which contain no Assur groups as subsets. Min- imal Assur groups provide a considerably improved basis of building-blocks, that have the least number of links and one dof joints, for the structural synthesis and selection of mechanisms. Aiming at hybrid robot design, we employ building-blocks derived from Assur groups. Let B be the degrees of freedom of the space in which a mechanism is intended to function, then Assur groups may be obtained Fig. 1. Some basic Assur groups. 986 A. Campos et al. / Mechanism and Machine Theory 43 (2008) 984–995 e1T Fig. 2. Null mobility kinematic chains. eliminating a link of a B-system kinematic chain with null mobility M = 0. For instance, the Assur groups in Fig. 1 may be obtained from the kinematic chains of Fig. 2 through this link elimination. These suitable null mobility chains may be designed applying the general mobility Gru¨ bler–Kutzbach criterion to a subset of n links and j single-freedom joints [23–25] M ? Ben j lTt j; M ? BL t j; where L = n + j + 1 is the number of independent loops in the chain. However, to comprise over constrained kinematic chains, i.e. chains where the same constrain is imposed more than once on a link (e.g. on the end effector), we may use a modified Gru¨ bler–Kutzbach criterion [26] which includes the number of over con- straints q M ? BL t j t q: e2T Generally speaking, over constrained mechanisms are potentially simpler and stiffer than statically deter- mined ones (they comprise fewer joints and distribute non-working loads to a great extent), even though they require higher construction accuracy and stricter tolerances in order to operate properly [27]. Using Eq. (2) for different numbers of loops (L > 0), over constraints (q > 0) and null mobility (M = 0) chains we obtain various couples (n, j) of links and joints that could form suitable kinematic chains in the screw system B, aiming at the generation of Assur groups. For instance, let L = 3, q = 0, M = 0 and B = 6, therefore the suitable kinematic chain must contain j = 18 single-freedom joints and n = 16 links. Different options to arrange a given couple (n, j) may be found through the partition [28] of the integer 2j into n parts, regarding that there is no link with just one joint. So, e.g. the partition of 2j = 36 joint halves (each joint is counted twice because the same joint appears in two links simultaneously) on n = 16 links is shown in Table 1 where 2n is a binary link, 3n is a ternary link and so on. In spite of all the options of Table 1 fulfilling the mobility criterion some of them are unsuitable to generate proper Assur groups for the generation of hybrid robots. Requirements for suitable kinematic chains for hybrid robots are introduced in Section 4. In the next section, based on the characteristics of Assur Groups, a synthesis method for hybrid kinematic chains is presented. Table 1 Partition of 2j = 36 ‘‘joints halves’’ into n = 16 links Link type 2n 3n 4n 5n 6n Option 1 12 4 – – – Option 2 13 2 1 – – Option 3 14 – 2 – – Option 4 14 1 – 1 – Option 5 15 – – – 1 A. Campos et al. / Mechanism and Machine Theory 43 (2008) 984–995 987 3. Hybrid kinematic chain design The presented method for hybrid kinematic chain design is based on the synthesis method introduced by Tischler [20] where Assur groups are used as fingers. Considering the characteristics of Assur groups, it is pos- sible to construct the simplest hybrid kinematic chains introducing Assur groups between the base and the end effector. Given that Assur groups may be formed by the elimination of a link in a suitable kinematic chain, simpler hybrid kinematic chains may be built by ‘‘cutting’’ a convenient link of a null mobility kinematic chain. So, one part of this link is considered the base and the other one is considered the end effector. Therefore, using this procedure the mobility of the hybrid chain is M = B q. For instance, consider a minimal kinematic chain with M = 0, L = 2, q = 0 and B = 3. Then the minimal kinematic chain must contain j = 6 single-freedom joints and n = 5 links. So, from the partition results that a possible chain consists of two ternary and three binary links. Fig. 3 presents two possible chains that result in two hybrid chains through the cutting of a suitable link. 4. Hybrid robot design In order to design hybrid robots that maintain the advantages of parallel structures, mentioned in Section 1, some considerations on hybrid kinematic chains must be observed. Sometimes, establishing these consider- ations is a step which depends more on intuition and imagination rather than on the ability to analyze. There- fore, different considerations could well arrive at a different final result. Let the hybrid robot mobility be M = Mf + Mm, where Mf and Mm are the number of fixed (to the base) and mobile drives, respectively. High stiffness and high force-to-weight ratio benefits of parallel structures are directly related to the drive positions. Best results are obtained when all the drives are fixed to the base, how- ever others low inertia arrangements as motors tilting with respect to the ground or attached at ball-screw tele- scopic legs are considered in this paper as fixed drives as well. Therefore, a suitable hybrid chain must contain at least a link with (Mf + 1) joints, to be the base, which will be cut according to the procedure introduced in Fig. 3. Procedure to obtain hybrid structures with M = 3 from suitable kinematic chains with M = 0, L = 2, q = 0 and B = 3. 988 A. Campos et al. / Mechanism and Machine Theory 43 (2008) 984–995 Fig. 4. Fractionated chains: (a) two closed sub-chains and (b) one open and one closed sub-chain. Section 3. Considering this base cut, that opens a loop, the number of loops in the M = 0 suitable chain (before the cutting) must be L = Mf. Through this cut the serial structure is created, so Mm consecutive joints must exist, which are driven by the mobile drives, between the cut and a non-binary link (the mobile base of the serial chain). Additionally, to set the fixed drives in a unique link, i.e. the base, the hybrid chain must not be a fraction- ated chain. A fractionated chain contains a link which divides the chain into two independent kinematic chains. These independent chains may be closed, i.e. every link is connected to at least two other links, or open as shown in Fig. 4. Regarding the manipulation task division remarked in Section 1, the position (translational DOF’s) and the orientation (rotational DOF’s) tasks are assigned to the parallel and to the serial structure of the hybrid chain, respectively. In general, for spatial tasks, this consideration drives us to place at least three fixed drives in the base Mf = 3. Another consideration that is important for hybrid robots is the symmetry which results in design advantages and simplicity of the velocity and acceleration calculations. At last, aiming at a general joint position in the space, the screw system for the hybrid robots is fixed to be B = 6. In the next section we apply the method to get hybrid structures as a whole. 5. Hybrid structures with 3, 4 and 5 fixed drives In order to illustrate the presented method, we implement it to obtain possibilities for a hybrid structure in the general space, i.e. M = B = 6. Aiming at advantages of parallel and serial structures we have at least Mf = 3 (to have at least three motors in the base), therefore the number of loops of the M = 0 suitable chain should be L = 3, 4 or 5. Hence, Eq. (2) results in several potential chains, with different numbers of links n and joints j. Each couple (n, j) may be arranged with different kind of links (binary, ternary, etc.), according to the partition. These options are detailed in Table 2 for q = 0, L = 3, 4 and 5. It is noted, through Eq. (2) and the partition, that if the value of q increases by one (one over constrained degree), the quantity of binary links decreases by one, and so on. For instance, the option q = 0, L = 3, 18 joints, 16 links (2n = 12 and 3n = 4) becomes q = 1, L = 3, 17 joints, 15 links (2n = 11 and 3n = 4). Considering the cut procedure and that at least Mf driven joints are required in the base at least one link with L + 1 (= 4, 5 or 6, respectively) or more joints to be the base is necessary. The options that do not fulfill this condition are unsuitable. Besides, those options in Table 2 that contain serial chains (sequence of binary links) between two joints of the same link are fractionated chains and unsuitable for hybrid robot design too, as shown in Fig. 5. A technique to avoid fractionated chains consists in jointing non-binary links (links with n > 2 joints) to the base through at least one but less than n serial chains. Applying the above criterions, only some chains (marked with gray columns in Table 2) are suitable to result in hybrid robots using the presented method. These chains are presented in a general form in Figs. 6–8 for L = 3, 4 and 5, respectively, where the number of binary links 2n depends on the number of over con- straints q P 0. A. Campos et al. / Mechanism and Machine Theory 43 (2008) 984–995 989 Table 2 Different options of couples (links, joints) (n, j) for chains with M = 0, L = 3, 4 and 5, q = 0 and B = 6, arranged for different kinds of links Suitable chains to generate hybrid robots are marked with gray columns. Fig. 5. Chains that present serial chains between two joints of the same link are fractionated. Fig. 6. Suitable chains with L = 3 to generate hybrid robots (through cuts in base): (a) 2n 6 13, 3n = 2 and 4n = 1; (b) 2n 6 14 and 4n = 2. 990 A. Campos et al. / Mechanism and Machine Theory 43 (2008) 984–995 Fig. 7. Suitable chains with L = 4 to generate hybrid robots (through cuts in base): (a) 2n 6 17, 3n = 3 and 5n = 1; (b) 2n 6 18, 3n = 1, and 4n = 1 and 5n = 1; (c) 2n 6 19 and 5n = 2. Fig. 8. Suitable chains with L = 5 to generate hybrid robots (through cuts in base): (a) 2n 6 21, 3n = 4 and 6n = 1; (b) 2n 6 22, 3n = 2, 4n = 1 and 6n = 1; (c) 2n 6 23, 4n = 2 and 6n = 1; (d) 2n 6 23, 3n = 1, 5n = 1 and 6n = 1; (e) 2n 6 24 and 6n = 2. The next step is to cut the base in such a way that a hybrid chain is obtained. It is important to notice that some cuts may produce the same hybrid chain, i.e. isomorphisms. For instance four different cuts in the base of the suitable chain in Fig. 6a result in the same hybrid chain as shown in Fig. 9. However, isomorphisms in this method may be detected through simple inspection due to the limited number (4, 5 or 6) of possible cuttings. Comparing only L + 1 = 4, 5 or 6 possible hybrid chains (one for each possible cut) it is possible to visually identify the existence of isomorphisms and reject them. Possible cuts which result in non-isomorphic hybrid chains are represented by a semicircle in Figs. 6–8. Fig. 9. Four possible different cuts produce the same hybrid chain: isomorphism. A. Campos et al. / Mechanism and Machine Theory 43 (2008) 984–995 991 Figs. 10–12 show the hybrid kinematic chains obtained through the presented method, with 3, 4 and 5 fixed drives in the base, respectively. These chains may be divided in symmetrical and non-symmetrical chains. In this paper we are interested in symmetrical chains due to the advantages cited above. From Figs. 10–12 we may observe that hybrid chains: a and b in Fig. 10, a.l, b.2 and c in Fig. 11 and b.1.1, d.l and e in Fig. 12 are symmetrical structures. It is important to notice that sometimes the symmetry is not obvious with only a glance and some effort is necessary to detect the symmetrical axis of the structure. For instance, the structures a in Fig. 10 and b.2 in Fig. 11 are rearranged in Fig. 13 to demonstrate their symmetry. Considering these symmetrical hybrid chains, three of them are typical hybrid robots, known parallel manipulators with a serial chain attached to their mobile platforms: Figs. 10b, 11c, and 12e. For instance see Fig. 14, where a serial chain with three rotative joints (for the orientation) is attached to the mobile plat- form of the fully parallel structure [14]. The completed structure may be designed from a null mobility chain with L = 3, q = 0, 2n = 14 and 4n = 2 (see Table 2 and Fig. 6). Additionally, the closed part of the hybrid chains a in Fig. 10, b.2 in Fig. 11 and d.l in Fig. 12 are observed in fully isotropic parallel mechanisms for Schoen?ies motion, i.e. a shaft (constant-speed-ratio coupling) is hinged to the mobile platform of a fully iso- tropic translational parallel manipulator [27]. To illustrate it, see the structure in Fig. 15 which corresponds to the closed part of a hybrid chain designed from a null mobility chain with L = 4, q = 3, 5n = 1, 4n = 1, 3n =1 and 2n = 15