机器人学导论课后习题答案
ContentsSolutions manualChapter 1-IntroductionChapter 2- Spatial descriptions and transformationsChapter 3- Manipulator Kinematics14Chapter 4-Inverse Manipulator Kinematics21Chapter 5-Jacobians: Velocities and Static ForcesChapter 6-Manipulator DynamicsChapter 7- Trajectory GenerationChapter 8- Manipulator Mechanism DesignChapter 9- Linear Control of manipulators59Chapter 10- Nonlinear Control of manipulatorsChapter 11- Force Control of Manipulators68Chapter 12- robot Programming languages and Systems72Chapter 13-Off-line Programming SystemsSolutions to the Programming Exercises(Parts 2-7, 9-11)75Matlab Exercises- solutions107MATLAB EXERCISE 2AMATLAB EXERCISE 2B112MATLAB EXERCISE 3119MATLAB EXERCISE 4MATLAB EXERCISE 5127MATLAB EXERCISE 6AMATLAB EXERCISE 6B135MATLAB EXERCISE 6C137MATLAB EXERCISE 7139MATLAB EXERCISE 8143MATLAB EXERCISE 9146Chapter 1PIntroductionExercises1.1) Here's just an example of a reasonable response(ref. [8] in Chap. 1)1955 Denavit Hartenberg developedMethodology for describing linkages1961George Devol patents design of rst robot1961First unimate robot installed1968 Shakey robot developed at S.R. I197Robot institute of A1975 Unimation becomes rst robot Co, to beotable1978 First Puma robot shippTotal U.s. market exceeds 500 milliordollars(annual revenueDevelopments might be split into a technical listd a business list1.2)(Based on 1981 numbersSource:Other-32.2%oL. Conigliaro, " robotics presentation, institutionalInvestors coMay 28, 1981, Bache NewsletterPalletize/Packaging-2.8%81-249lachining-6.8%Material Handling-11.8%Assembly-22.4%Welding.9%13)People Are FlexibleBut More Expensive Every YearS60U.S. Automotives50s40U.S. ElectronicS20 Robot Labor(2 shiftsU.S. Food10KoreaSO11971741811會1995No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher t as they currently existo 2005 Pearson Education, Inc, Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright lav4 Kingmanstudy of posind derivatiof position without regard to forces which causethe motion. Workspace is the locus of positionsand orientations achievable by the end-effector ofa manipulator. Trajectory is a time based functionwhich specifies the position(and higher derivatives)of the robot mechanism for any value oftime1.5) Frame is a coordinate system, usually specified inposition and orientation relative to some imbedding frame. Degrees of freedom is the numberof independent variables which must be specifiedin order topletely locate all members of a(rigid-body) mechanism. Position control impliesthe use of a control system, usually in a closedloop manner, to control the position of one ormore moving bodies.1.6) Force control is the use of (usually closedalgorithms to control the forces of contact generated when a robot touches its work environmentA robot programming language is a programminglanguage intended for use in specifying manipulator actions1.7) Structural stiffness is the“KinF=K△X(A.KAHookes law" )which describes the rigidity ofsome structure. Nonlinear control refers to a closedloop control system in which either the systemo be controlled, or the control algorithm itself isnonlinear in nature. Off line programming is theprocess of creating a program for a device withoutccess to that device1. 8)See references. For example, in 1985 average laborcosts of 15 to $20 per hour are reasonable(dependinghow fringe benefits are calculated)1.9)Obviously it has increased dramatically. Recently(1988-1990)the ratio doubles or even triples eachear1.10) See Figure 1.3, but use latest data you can find2No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher s as they currently existo 2005 Pearson Education, Inc, Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright lavChapterSpatial descriptions and TransformationsExercises2.1)R=rot(,φ)rot(,0)ce0Cφ-$φS0SpCd儿L03ceS日CφS6CφC6-SφS中S9S中C6C中22)R=ro(,45°)ro(,30°)0866050.707-.7070.707.70750.86653707-.612537076122.3) Since rotations are performed about axes of theframe being rotated, these are Euler-Angle styleR=rot(,0)rot(x,φ)We might also use the following reasoningR(,中)=6R-(e=[rot(,-中)rot(,-0)]-1-D)rotrot(,)rot(x,中)Yet another way of viewing the same operation1st rotate by rot(,θ)2nd rotate by rot(i, O)rot(i, oNo portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher s as they currently existo 2005 Pearson Education, Inc, Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright lav2.3)(continued(This is a similarity transformComposing thesc two rotationsrot(,O)rot(x,φ)rot-1(z,0)·rot(3,0)(,0)rot(x,φ)C6-S601「10SeCe00Cφ-S0010SφCφC6 -SACp SA SocAC -ce so0Cφ2.4) This is the same as 2.3 only with numbersR=rot(,30°)ro(,45)50612-6120707.7072.5) If Vi is an eigenvector of R, thenRV=7VIf the cigenvalue associated with Vi is 1, thenRVi= ViHence the vector is not changed by the rotation rSo V is the axis of rotation2.6) Imagine a frame (a) whose i axis is aligned withthe direction kThen the rotation with rotates vectors about k byo degrees could be written:X,KR=URrot(AZ, O)AR [1]We write the description of (A) in () asABCD KURE KF KIf we multiply out Eq. [1]above, and then simplifyIsing A2+B2+C2=1, D'+E2+F2=1, [ABC]IDEF=O, LABCJO DEF]=[KKyk, we arriveat Eq(2. 80 )in the book. Also, see [R. Paul]*No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher s as they currently existo 2005 Pearson Education, Inc, Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright lavRRRRRRR132.7) Let R=RR233(1) Compute R1l+r22+R33= N(2) IfN=3, then 0= A cosincerotation is zero, K is arbitraryIf N=-l, then 6= A cos(-1)=180. Inthis case eq(2.80)becomes2K2-=1 2K-K. 2K.Kro(R,180)=2K,K,2K2-12K,K2KK, 2KK 2K-1K2-1=R1→Kx=±√(R1+1)/22KxKy=R1→Ky=R12/2K2KxKz=R31→Kz=R3/2KxHowever, if.20. then this is ill-definedso use a different column for solution(notthe first column as above)(4)If -1
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