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运动链机械手
机械手运动链
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外文翻译-关于机械手的运动链：刚度和夹紧,运动链机械手,机械手运动链
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Kinematic chains for robot hands: Grasp and rigidity A. Srinath a, A.C. Raob,* a Mechanical Engineering, PVP Siddhartha Institute of Technology, Vijayawada, AndhraPradesh, India b Sai Spurthi Institute of Technology, Gangaram, Sathupally, Khammam District, AndhraPradesh 507 303, India Received 30 July 2005; received in revised form 1 June 2006; accepted 8 June 2006 Available online 17 August 2006 Abstract A variety of kinematic chains exists which can be considered for application as robot hands. The designer must have a tool to know relatively which of them will possess greater grasp and rigidity. In this paper a numerical measure to estimate parallelism between the object and ground link (of the hand) is proposed. This measure can be used to compare the robot hands for grasp and rigidity. ? 2006 Elsevier Ltd. All rights reserved. 1. Introduction It is well known that closed kinematic chains with multi-degree-of-freedom (d.o.f) are potential candidates for application as planar parallel robots when greater rigidity is required 16. Also linkages can be used as robot hands consisting of fi ngers and fi nger tips 7. In order to choose one from the available chains the designer must know their characteristics like grasp and rigidity at the conceptual stage of design. Presently, selection of the type and number of fi ngers etc., depends upon the intuition of the designer. Recently the author 6 has presented a method to estimate parallelism between various links of a kinematic chain which in turn is indicative of rigidity. Grasp depends upon the number of fi ngers and the parallelism that exists between them. Some times a fi n- ger may have more than one tip. Obviously, grasp is also infl uenced by the extent (degree) of parallelism between the object and the ground (fi xed) link of the robot hand. Greater parallelism leads to greater grasp and rigidity. Some of the robot hands developed by Tischler et al. 7 are shown in Fig. 7. In, what follows, a new expres- sion is proposed to measure the parallelism between the links of a chain. The results obtained by the proposed method coincide exactly with those obtained by the method in Ref. 6. The same is applied to rate the various hands shown in Fig. 7. 0094-114X/$ - see front matter ? 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2006.06.009 * Corresponding author. Tel.: +91 592 281 023; fax: +91 592 281 422. E-mail address: sssitrediff (A.C. Rao). Mechanism and Machine Theory 42 (2007) 691697 /locate/mechmt Mechanism and Machine Theory 2. Measure for parallelism Parallelism between the links of a chain means that motion is transmitted from one link to the other through two or more independent paths. Links of every closed kinematic chain are parallely connected; the extent of parallelism between the links may be diff erent. Consider the simple four-bar chain in Fig. 1. It is evident that of the links 1 and 3 are par- allely connected through links 2 and 4. Same is true with the links 2 and 4. Parallelism will be present as long as there are two or more paths between links. However, Parallelism decreases as the number of links separat- ing them increase. For, example, consider Fig. 2. Parallelism exists between links 1 and 2 but the parallelism is less compared to that the links 1 and 3 of Fig. 1 i.e., more the separation between the concerned links, greater is the tendency to become serial. Parallelism between the links reduces as the size of the closed loop increases i.e., parallelism between the links of a fi ve-bar loop shown in Fig. 4 will be lesser than those in a four-bar loop. Parallelism can be viewed primarily as a loop size expressed by, four-bar loop, fi ve-bar loop etc.; lesser the size of the loop, greater is the parallelism. Now the parallelism between any two links of a loop can be understood in the following manner. Maximum number of joints in a loop is equal to the loop size i.e., four in a four-bar loop etc.,. In order to study paral- lelism between two links in a loop, the independent paths between the links must be located. As per the graph theory, size of the path is defi ned as the number of joints that separate the two links (along the shortest path). Independent path means that no joint should be common to two or more paths. In a four-bar loop, Fig. 1, link-3 is separated from link-1 by two joints each along the two independent paths i.e., via link-2 and via link-4. It is said earlier that the parallelism between links depends upon the number of links or joints that separate them along each path, parallelism reducing with increase of such joints. If the total number of joints in a loop is J, then the number of joints along the paths i, j etc., are, respectively, Ji, Jj; such that Ji Jj . J The farthest link having least parallelism is the one for which the product Ji, Jjis the maximum possible. In view of this, the following relation can express parallelism P between two links k and l in a loop. Pkl L=Ji? Jj;1 where L is the loop size and Jiand Jjare the number of joints along independent paths i and j between the links k and l. Fig. 1. Four-bar chain. Fig. 2. Five-bar chain. 692A. Srinath, A.C. Rao / Mechanism and Machine Theory 42 (2007) 691697 For example, P13of the four-bar loop, Fig. 1, P13 4=2 ? 2 1;a P12 4=1 ? 3 1:33;b It may be visualized that the parallelism between links 1 and 3 is one and that between links 1 and 2 is more because of direct adjacency. Similarly, in a fi ve-bar loop, Fig. 2, P12 5=1 ? 4 1:25 P13 P14 5=2 ? 3 0:83 In multi loop chains, two links may be separated by more than one loop, Fig. 3. Links 1 and 4 are separated by three loops (1)(3). 3. How the parallelism matters Consider three link-rigid frame, Fig. 4 parallelism between links say 1, 2 is P12 3=1 ? 2 3=2: Parallelism between every pair of links is the same in the above case. It is easy to see that the links 13 are immobile which can be attributed to greater parallelism between links. Consider Fig. 5 which is a rigid chain. Using the relation (1), Fig. 3. Eight-bar chain. Fig. 4. Three-bar chain. Fig. 5. Five-bar rigid frame. A. Srinath, A.C. Rao / Mechanism and Machine Theory 42 (2007) 691697693 P13 Parallelism between links 1 and 3 4 2 ? 2 4 2 ? 2 ? 1 2 3 2 In general, it can be said that if parallelism between two links is equal or greater than 3/2 then the links are immobile. Such possibility occurs only in degenerate chains. In chains with d.o.f. 0 motion between links is possible even if the parallelism between links is equal to or greater than 3/2; for example, parallelism P14in Fig. 3 is greater than 3/2. It is understood that greater parallelism between two links leads to greater stiff ness, a property useful to the designer when he considers kinematic chains for application as manipulators. In such cases and in most gen- eral form parallelism, Pij= 1 indicates that the links I and j will have equal or near equal (angular) speeds while Pij 1 indicates greater speed ratio between the links. 4. Interpretation Though two links are considered serially connected, say links 1 and 3, Fig. 6, the second path necessary for parallelism to exist between those links 1 and 3 is considered to consist of very large number of links and joints (shown in dotted lines). Eq. (3) when applied gives parallelism between the links 1 and 3. In this case P13= 1/2. Eq. (2) also leads to the same result. In other words, parallelism between two links can also be considered as links in series separated by the number of joints equal to the inverse of the parallelism. 5. Application to robot hands Consider the robot hand (2) of Fig. 7. This hand has two fi ngers and three fi nger tips. This fi gure is redrawn as Fig. 8 for convenience. Links are numbered 1, 2 etc. p, q and r are the fi nger tips which make point contact with the object (o). Fingers are indicated by a and b. Frictional point contact between the grasped object and Fig. 6. Equivalent graph. Parallelism between two links I and j can be expressed by the relation Pij X parallelism due to each loop in which links i and j participate ? X 1=Number of joints common to apairof adjacent loops in which links I and j participate: 2 Parallelism between two links I and j can also be expressed by the relation given in Ref. 6 i.e., Pij X m k1 1=Jk3 where, Jk= number of joints along path k between the links I and j. For example, P14in Fig. 3 = 1/2 + 1/2 + 1/3 + 1/3 = 1 2/3 694A. Srinath, A.C. Rao / Mechanism and Machine Theory 42 (2007) 691697 the fi nger tips can be considered equivalent to spherical joints between the object and the fi nger tips 8. In planar hands, these joints will be reduced to revolute joints. Since the fi nger a has two tips p and q, the parallelism between the object and the ternary link 6 may be estimated fi rst by using Eq. (2) and then combined with the rest of the link assembly. Considering points p, q and r as a part of three-bar loop and using Eq. (2), parallelism P60between link-6 and the object (o) can be expressed as P60 3=1 ? 2 3=2 following the explanation given in Section 4, the assembly of the links 6 and 7 can be replaced by a single binary link-6 grasping the object with a joint value of 2/3. With this understanding, Fig. 8 can be considered Fig. 7. Robot hands. A. Srinath, A.C. Rao / Mechanism and Machine Theory 42 (2007) 691697695 equivalent to Fig. 9 with a joint at point-A having a numerical value of 2/3 while all other revolute joints are of value of one (1) each. In order to apply Eq. (2) to estimate parallelism between links, the size of the loop in which the two links participate must be known. Recalling that size of the lop is equal to the number of joints, the size of the loop consisting of links 1, 2; Object, , 10 should be taken as 9 2/3 bar-loop since the equivalent joint at point A is of value 2/3 i.e., inverse of the parallelism between the ternary link 6 and (o); the Object. Now, applying Eq. (2), P10 i:e:; parallelism between the link-1 and the objecto 92=3 ? 1=52=3 ? 1=4 0:425 As a second example consider the robot hand (e) of Fig. 7 parallelism between the ternary link and the object 5=3 ? 2 5=6 Thus the link assembly above the ternary link can be replaced by a binary link with a joint value of 6/5 between the object and this (equivalent) binary link. Thus, the total number of joints in the remaining assembly will be 8 1/5. Hence the loop size will be 8 1/5. Now applying Eq. (2), P10 parallelism between the ground link 1 and the object 81=5 ? 1=41=5 ? 1=4 0:488 Similarly, parallelism of all the robot hands, Fig. 7, are determined. Robot hands with greater parallelism will be more rigid and have greater grasp. Table 1 shows the parallelism, in descending order. Fig. 8. Robot hand (a) of Fig. 7. Fig. 9. Equivalent robot hand. 696A. Srinath, A.C. Rao / Mechanism and Machine Theory 42 (2007) 691697 6. Conclusion A simple method to estimate parallelism between the ground link of the robot hand and the object is pre- sented. The same is used to rate the robot hands given in Fig. 7. A diff erent method 6 when applied to the robot hands, Fig. 7 gave the same results. The results presented here can be considered accurate because of the fact that when equivalent joint value, usually a fraction, is considered, the size of the loop is also changed to include the equivalent joint value which is a prerequisite in developing Eq. (2). Greater parallelism leads to greater grasp and rigidity. Unit parallelism between two links indicate that they are likely to have unit velocity ratio while greater parallelism indicates the possibility of high speed ratio. Dimensions, of course decide the exact speed ratio but the parallelism infl uences as pointed above. References 1 K.H. Hunt, Structural kinematics of in-parallel actuated robot arms, ASME Journal of Mechanisms, Transmission and Automation in Design 105 (4) (1983) 705712. 2 G.R. Pennock, D.J. Dassner, Kinematic analysis of a planar eight-bar linkage application to a platform type robot, ASME Journal of Mechanical Design 144 (1992) 8795. 3 C.V. Parenti, C. Innocenti, Forward Displacement Analysis of parallel mechanisms: closed form solution of PPR 3S structures, ASME Journal of Mechanical Design 144 (1992) 6872. 4 A.C. Rao, Jagadeesh Anne, Topology based characteristics of kinematic chains; work space, rigidity, input-joint and isomorphism, Mechanism and Machine Theory 33 (1998) 625638. 5 A.C. Rao, Topological characteristics of linkage mechanisms with particular reference to platform type robots, Mechanism and Machine Theory 30 (1995) 3342. 6 A.C. Rao, Parallelism in planar manipulators: a measure, Trans ASME, Journal of Mechanical Design 128 (2006). 7 C.R. Tischler, A.E. Samuel, K.H. Hunt, Kinematic chains for robot hands II, Mechanism and Machine Theory 30 (8) (1995) 12201224. 8 J.J. Craig, Introduction to Robotics, Second ed., Pearson Education (Singapore) Pvt. Ltd, 2003. Table 1 Robot hands of Fig. 7Parallelism i0.75 h0.61 g0.535 f0.525 c0.52 e0.48 b0.46 d0.45 a0.425 A. Srinath, A.C. Rao / Mechanism and Machine Theory 42 (2007) 691697697 关于机械手的运动链：刚度和夹紧摘要 各种运动联的存在主要考虑机械手的运用。设计师要有一个工具,他们将比较了解和把握更多关于刚度和夹紧的知识。本文提出数值计算并测量物体与地面之间的连接(机械手)。这一措施可用于机器手的刚度和夹紧。1.引言： 这是众所周知的,封闭运动链多自由度(自由度)的可能人选为平面并联机器人的应用 当需要刚度和夹紧。也可作为联系组成的机器手刀架及刀架尖端。为了选择一个有效链条，在概念设计阶段设计师必须知道刚度和夹紧的参数。目前,选择刀架的类型和数量等，取决于设计者的计算。近日编者提示一种方法来估算各环节之间的链条运动。 夹紧多少取决于刀架和它们之间存在的平行。有的时候,刀架可能不止一个尖端。显然 夹紧程度也受并行性(度)及地面物体之间的联系(固定)的机器手的影响。 一些机器手由蒂森科研制等。显示在图7。而接下来,提出了新的表述是衡量一个环节之间平行链条。该方法的结果完全吻合方法与所得的13. 6.同样适应于各种机械手如图7。2.并行测量： 并行环节之间的链条意味着运动是由一个传递给其他两个环节以上独立路径。 每个环节都是封闭运动链平行相连；并行之间联系的程度可能不同。考虑简单四杆链如图1。显然，1和3并行连接通过并行连接2和4。同样的环节2、4。并行只要有两个或两个以上路径之间的联系。但是，由于一些环节并行跌幅增加使他们分开。例如考虑图2。并行之间存在联系，但1至2并行比较少,通1和3 如图1，即更多的关注之间的联系分离，成为大趋势是串行。并行之间的联系降低了闭环升幅大小即并行之间联系的五杆回路如图4， 将越来越少四杆回路。 并行可作为回路主要尺寸表示，四杆回路、五杆回路等； 规模较小的回路，更是并行。 现在有两个环节之间的并行，可以理解一个环路，以下述方式。最多回路连接同样取决回路的大小，即在四个四杆回路等。 为了研究两个环节之间的并行回路，独立路径之间的联系必然的。 按图论，大小道路数定义为分开的两通接头(沿最短路径)。联合意味着没有独立的道路应为两个以上的共同道路。在四杆回路如图1，连三分开连接两个节点分别沿一两个独立路径即 经联系，并通过连接2-4。这是刚才说的并行之间的联系取决于多项链条，或分开沿线各道路，以增加并行性，降低此类接头。如果一个节点在回路J号，然后许多节点在回路I、J等；象这样Ji + Jj + . . .=J最远的是并行连接至少有一种产品 Ji, Jj是最大限度。有鉴于此,就可以表达以下两种并行连接K和L在仪回路。PklL/(Ji*Jj)； (1)其中L是回路大小Ji和Jj大量的节点进行独立回路i和j之间连接k和l回路。 图1、四杆机构 图2、五杆机构 图3、八杆机构例如, P13的四杆回路，图1。P13=4/(22)=1， (a)P12=4/(13)=1:33， (b)可以说并行直接之间的联系是1和3之间的联系,并与1和2是因为直接邻接。同样，在五杆回路，图2。 P12=5/(14)=1.25P13=P14=5/(23)=0.83多支链，可隔着两个环节多回路，图3，节点1和4通隔三环路(1)-(3)。3.如何并行事项考虑三个连接刚架，图4，四环节并行之间节点象说1，2一样。P123/(12)=3/2，每一个节点是一对并行关系与上述同一案件。不难看出，连动1-3可归咎于并行之间的联系。考虑图5是刚性机构，
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