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E-raamat: Kinematics of General Spatial Mechanical Systems

(METU (Middle East Technical University), Ankara, Turkey)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 11-Mar-2020
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119195764
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Kinematics of General Spatial Mechanical SystemsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 11-Mar-2020
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119195764
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Guide to kinematic theory for the analysis of spatial mechanisms and manipulators

Kinematics of General Spatial Mechanical Systems is an effective and proficient guide to the kinematic description and analysis of the spatial mechanical systems such as serial manipulators, parallel manipulators and spatial mechanisms. The author highlights the analytical and semi-analytical methods for solving the relevant equations and considers four main elements: The mathematics of spatial kinematics with the necessary theorems, formulas and methods; The kinematic description of the links and joints including the rolling contact joints; Writing the kinematic chain and loop equations for the systems to be analyzed; and Solving these equations for the unspecified variables both in the forward and inverse senses together with the multiplicity and singularity analyses.

Comprehensive in scope, the book covers topics ranging from rather elementary subjects such as spatial mechanisms with single degree of freedom to more advanced topics such as serial manipulators including redundant and deficient ones, parallel manipulators, and non-holonomic spatial cam mechanisms that involve rolling without slipping motions. The author presents an effective and accessible symbolic manipulation method making it possible to obtain neat and transparent expressions that describe the systems showing all the kinematic details. Such expressions readily lead to analytical or semi-analytical solutions. They also facilitate the identification and analysis of the multiplicities and singularities. 

This all-time beneficial book:

  • Provides an easy-to-use systematic formulation method that is applicable to all sorts of spatial machanisms and manipulators
  • Introduces a symbolic manipulation method, which is effective and straightforward to use, so that kinematic relationships can be simplified by using all the special geometric features of the system
  • Offers an accessible format that uses a systematic and easy-to-conceive notation which has proven successful
  • Presents content written by an author who is a renowned expert in the field
  • Includes an accompanying website

Written for academicians, students, engineers, computer scientists and any other people working in the area of spatial mechanisms and manipulators, Kinematics of General Spatial Mechanical Systems provides a clear notation, formulation, and a logical approach to the topic and offers a fresh presentation of challenging material.

Preface xv
Acknowledgments xix
List of Commonly Used Symbols, Abbreviations, and Acronyms
xxi
About the Companion Website xxvii
1 Vectors and Their Matrix Representations in Selected Reference Frames
1(12)
1.1 General Features of Notation
1(1)
1.2 Vectors
2(1)
1.2.1 Definition and Description of a Vector
2(1)
1.2.2 Equality of Vectors
2(1)
1.2.3 Opposite Vectors
3(1)
1.3 Vector Products
3(1)
1.3.1 Dot Product
3(1)
1.3.2 Cross Product
3(1)
1.4 Reference Frames
4(2)
1.5 Representation of a Vector in a Selected Reference Frame
6(1)
1.6 Matrix Operations Corresponding to Vector Operations
7(2)
1.6.1 Dot Product
7(1)
1.6.2 Cross Product and Skew Symmetric Cross Product Matrices
8(1)
1.7 Mathematical Properties of the Skew Symmetric Matrices
9(1)
1.8 Examples Involving Skew Symmetric Matrices
10(3)
1.8.1 Example 1.1
10(1)
1.8.2 Example 1.2
11(1)
1.8.3 Example 1.3
11(2)
2 Rotation of Vectors and Rotation Matrices
13(18)
2.1 Vector Equation of Rotation and the Rodrigues Formula
13(2)
2.2 Matrix Equation of Rotation and the Rotation Matrix
15(1)
2.3 Exponentially Expressed Rotation Matrix
16(1)
2.4 Basic Rotation Matrices
16(1)
2.5 Successive Rotations
17(1)
2.6 Orthonormality of the Rotation Matrices
18(2)
2.7 Mathematical Properties of the Rotation Matrices
20(2)
2.7.1 Mathematical Properties of General Rotation Matrices
20(2)
2.7.2 Mathematical Properties of the Basic Rotation Matrices
22(1)
2.8 Examples Involving Rotation Matrices
22(3)
2.8.1 Example 2.1
22(1)
2.8.2 Example 2.2
23(1)
2.8.3 Example 2.3
24(1)
2.8.4 Example 2.4
24(1)
2.9 Determination of the Angle and Axis of a Specified Rotation Matrix
25(4)
2.9.1 Scalar Equations of Rotation
25(1)
2.9.2 Determination of the Angle of Rotation
26(1)
2.9.3 Determination of the Axis of Rotation
26(3)
2.9.4 Discussion About the Optional Sign Variables
29(1)
2.10 Definition and Properties of the Double Argument Arctangent Function
29(2)
3 Matrix Representations of Vectors in Different Reference Frames and the Component Transformation Matrices
31(32)
3.1 Matrix Representations of a Vector in Different Reference Frames
31(1)
3.2 Transformation Matrices Between Reference Frames
32(2)
3.2.1 Definition and Usage of a Transformation Matrix
32(1)
3.2.2 Basic Properties of a Transformation Matrix
33(1)
3.3 Expression of a Transformation Matrix in Terms of Basis Vectors
34(3)
3.3.1 Column-by-Column Expression
34(1)
3.3.2 Row-by-Row Expression
34(1)
3.3.3 Remark 3.1
35(1)
3.3.4 Remark 3.2
35(1)
3.3.5 Remark 3.3
36(1)
3.3.6 Example 3.1
36(1)
3.4 Expression of a Transformation Matrix as a Direction Cosine Matrix
37(1)
3.4.1 Definitions of Direction Angles and Direction Cosines
37(1)
3.4.2 Transformation Matrix Formed as a Direction Cosine Matrix
38(1)
3.5 Expression of a Transformation Matrix as a Rotation Matrix
38(2)
3.5.1 Correlation Between the Rotation and Transformation Matrices
38(1)
3.5.2 Distinction Between the Rotation and Transformation Matrices
39(1)
3.6 Relationship Between the Matrix Representations of a Rotation Operator in Different Reference Frames
40(1)
3.7 Expression of a Transformation Matrix in a Case of Several Successive Rotations
40(2)
3.7.1 Rotated Frame Based (RFB) Formulation
41(1)
3.7.2 Initial Frame Based (IFB) Formulation
41(1)
3.8 Expression of a Transformation Matrix in Terms of Euler Angles
42(15)
3.8.1 General Definition of Euler Angles
42(1)
3.8.2 IFB (Initial Frame Based) Euler Angle Sequences
42(1)
3.8.3 RFB (Rotated Frame Based) Euler Angle Sequences
43(1)
3.8.4 Remark 3.4
44(1)
3.8.5 Remark 3.5
44(1)
3.8.6 Remark 3.6: Preference Between IFB and RFB Sequences
45(1)
3.8.7 Commonly Used Euler Angle Sequences
45(1)
3.8.8 Extraction of Euler Angles from a Given Transformation Matrix
46(11)
3.9 Position of a Point Expressed in Different Reference Frames and Homogeneous Transformation Matrices
57(6)
3.9.1 Position of a Point Expressed in Different Reference Frames
51(1)
3.9.2 Homogeneous, Nonhomogeneous, Linear, Nonlinear, and Affine Relationships
52(1)
3.9.3 Affine Coordinate Transformation Between Two Reference Frames
53(1)
3.9.4 Homogeneous Coordinate Transformation Between Two Reference Frames
54(1)
3.9.5 Mathematical Properties of the Homogeneous Transformation Matrices
55(3)
3.9.6 Example 3.2
58(5)
4 Vector Differentiation Accompanied by Velocity and Acceleration Expressions
63(18)
4.1 Derivatives of a Vector with Respect to Different Reference Frames
63(3)
4.1.1 Differentiation and Resolution Frames
63(1)
4.1.2 Components in Different Differentiation and Resolution Frames
64(1)
4.1.3 Example
65(1)
4.2 Vector Derivatives with Respect to Different Reference Frames and the Coriolis Transport Theorem
66(4)
4.2.1 First Derivatives and the Relative Angular Velocity
66(2)
4.2.2 Second Derivatives and the Relative Angular Acceleration
68(2)
4.3 Combination of Relative Angular Velocities and Accelerations
70(1)
4.3.1 Combination of Relative Angular Velocities
70(1)
4.3.2 Combination of Relative Angular Accelerations
71(1)
4.4 Angular Velocities and Accelerations Associated with Rotation Sequences
71(6)
4.4.1 Relative Angular Velocities and Accelerations about Relatively Fixed Axes
71(1)
4.4.2 Example
72(2)
4.4.3 Angular Velocities Associated with the Euler Angle Sequences
74(3)
4.5 Velocity and Acceleration of a Point with Respect to Different Reference Frames
77(4)
4.5.1 Velocity of a Point with Respect to Different Reference Frames
77(1)
4.5.2 Acceleration of a Point with Respect to Different Reference Frames
78(1)
4.5.3 Velocity and Acceleration Expressions with Simplified Notations
79(2)
5 Kinematics of Rigid Body Systems
81(44)
5.1 Kinematic Description of a Rigid Body System
82(2)
5.1.1 Body Frames and Joint Frames
82(1)
5.1.2 Kinematic Chains, Kinematic Branches, and Kinematic Loops
83(1)
5.1.3 Joints or Kinematic Pairs
83(1)
5.2 Position Equations for a Kinematic Chain of Rigid Bodies
84(3)
5.2.1 Relative Orientation Equation Between Successive Bodies
85(1)
5.2.2 Relative Location Equation Between Successive Bodies
85(1)
5.2.3 Orientation of a Body with Respect to the Base of the Kinematic Chain
85(1)
5.2.4 Location of a Body with Respect to the Base of the Kinematic Chain
86(1)
5.2.5 Loop Closure Equations for a Kinematic Loop
86(1)
5.3 Velocity Equations for a Kinematic Chain of Rigid Bodies
87(3)
5.3.1 Relative Angular Velocity between Successive Bodies
87(1)
5.3.2 Relative Translational Velocity Between Successive Bodies
88(1)
5.3.3 Angular Velocity of a Body with Respect to the Base
89(1)
5.3.4 Translational Velocity of a Body with Respect to the Base
89(1)
5.3.5 Velocity Equations for a Kinematic Loop
90(1)
5.4 Acceleration Equations for a Kinematic Chain of Rigid Bodies
90(4)
5.4.1 Relative Angular Acceleration Between Successive Bodies
91(1)
5.4.2 Relative Translational Acceleration Between Successive Bodies
92(1)
5.4.3 Angular Acceleration of a Body with Respect to the Base
92(1)
5.4.4 Translational Acceleration of a Body with Respect to the Base
93(1)
5.4.5 Acceleration Equations for a Kinematic Loop
93(1)
5.5 Example 5.1: A Serial Manipulator with an RRP Arm
94(12)
5.5.1 Kinematic Description of the System
94(1)
5.5.2 Position Analysis
95(5)
5.5.3 Velocity Analysis
100(3)
5.5.4 Acceleration Analysis
103(3)
5.6 Example 5.2: A Spatial Slider-Crank (RSSP) Mechanism
106(19)
5.6.1 Kinematic Description of the Mechanism
106(2)
5.6.2 Loop Closure Equations
108(1)
5.6.3 Degree of Freedom or Mobility
109(1)
5.6.4 Position Analysis
110(9)
5.6.5 Velocity Analysis
119(3)
5.6.6 Acceleration Analysis
122(3)
6 Joints and Their Kinematic Characteristics
125(60)
6.1 Kinematic Details of the Joints
125(2)
6.1.1 Description of a Joint as a Kinematic Pair
125(1)
6.1.2 Degree of Freedom or Mobility of a Joint
126(1)
6.1.3 Number of Distinct Joints Between Two Rigid Bodies
126(1)
6.1 A Classification of the Joints
127(1)
6.2 Typical Lower Order Joints
128(4)
6.2.1 Single-Axis Joints
128(2)
6.2.2 Universal Joint
130(1)
6.2.3 Spherical Joint
131(1)
6.2.4 Plane-on-Plane Joint
132(1)
6.3 Higher Order Joints with Simple Contacts
132(2)
6.3.1 Line-on-Plane Joint
132(1)
6.3.2 Point-on-Plane Joint
133(1)
6.3.3 Point-on-Surface Joint
133(1)
6.4 Typical Multi-Joint Connections
134(4)
6.4.1 Fork-on-Surface Joint
134(2)
6.4.2 Triangle-on-Surface Joint
136(2)
6.5 Rolling Contact Joints with Point Contacts
138(10)
6.5.1 Surface-on-Surface Joint
138(6)
6.5.2 Curve-on-Surface Joint
144(3)
6.5.3 Curve-on-Curve Joint
147(1)
6.6 Rolling Contact Joints with Line Contacts
148(19)
6.6.1 Cone-on-Cone Joint
148(7)
6.6.2 Cone-on-Cylinder Joint
155(2)
6.6.3 Cone-on-Plane Joint
157(4)
6.6.4 Cylinder-on-Cylinder Joint
161(3)
6.6.5 Cylinder-on-Plane Joint
164(3)
6.7 Examples
167(10)
6.7.1 Example 6.1: An RRRSP Mechanism
167(4)
6.7.2 Example 6.2: A Two-Link Mechanism with Three Point-on-Plane Joints
171(3)
6.7.3 Example 6.3: A Spatial Cam Mechanism
174(3)
6.7 A Example 6.4: A Spatial Cam Mechanism That Allows Rolling Without Slipping
177(8)
7 Kinematic Features of Serial Manipulators
185(14)
7.1 Kinematic Description of a General Serial Manipulator
185(1)
7.2 Denavit-Hartenberg Convention
186(1)
7.3 D--H Convention for Successive Intermediate Links and Joints
187(3)
7.3.1 Assignment and Description of the Link Frames
187(1)
7.3.2 D--H Parameters
188(1)
7.3.3 Relative Position Formulas Between Successive Links
189(1)
7.3.4 Alternative Multi-Index Notation for the D-H Convention
189(1)
7.4 D--H Convention for the First Joint
190(3)
7.5 D--H Convention for the Last Joint
193(2)
7.6 D--H Convention for Successive Joints with Perpendicularly Intersecting Axes
195(1)
7.7 D-H Convention for Successive Joints with Parallel Axes
195(2)
7.8 D-H Convention for Successive Joints with Coincident Axes
197(2)
8 Position and Motion Analyses of Generic Serial Manipulators
199(34)
8.1 Forward Kinematics
201(1)
8.2 Compact Formulation of Forward Kinematics
202(1)
8.3 Detailed Formulation of Forward Kinematics
203(2)
8.4 Manipulators with or without Spherical Wrists
205(2)
8.5 Inverse Kinematics
207(1)
8.6 Inverse Kinematic Solution for a Regular Manipulator
208(4)
8.6.1 Regular Manipulator with a Spherical Wrist
208(3)
8.6.2 Regular Manipulator with a Nonspherical Wrist
211(1)
8.7 Inverse Kinematic Solution for a Redundant Manipulator
212(2)
8.7.1 Solution by Specifying the Variables of Certain Joints
212(1)
8.7.2 Solution by Optimization
213(1)
8.8 Inverse Kinematic Solution for a Deficient Manipulator
214(1)
8.8.1 Compromise in Orientation in Favor of a Completely Specified Location
214(1)
8.8.2 Compromise in Location in Favor of a Completely Specified Orientation
215(1)
8.9 Forward Kinematics of Motion
215(3)
8.9.1 Forward Kinematics of Velocity Relationships
215(1)
8.9.2 Forward Kinematics of Acceleration Relationships
216(2)
8.10 Jacobian Matrices Associated with the Wrist and Tip Points
218(2)
8.11 Recursive Position, Velocity, and Acceleration Formulations
220(3)
8.11.1 Orientations of the Links
220(1)
8.11.2 Locations of the Link Frame Origins
221(1)
8.11.3 Locations of the Mass Centers of the Links
221(1)
8.11.4 Angular Velocities of the Links
221(1)
8.11.5 Velocities of the Link Frame Origins
222(1)
8.11.6 Velocities of the Mass Centers of the Links
222(1)
8.11.7 Angular Accelerations of the Links
222(1)
8.11.8 Accelerations of the Link Frame Origins
222(1)
8.11.9 Accelerations of the Mass Centers of the Links
223(1)
8.12 Inverse Motion Analysis of a Manipulator Based on the Jacobian Matrix
223(2)
8.12.1 Inverse Velocity Analysis of a Regular Manipulator
224(1)
8.12.2 Inverse Acceleration Analysis of a Regular Manipulator
225(1)
8.13 Inverse Motion Analysis of a Redundant Manipulator
225(4)
8.13.1 Inverse Velocity Analysis
225(3)
8.13.2 Inverse Acceleration Analysis
228(1)
8.14 Inverse Motion Analysis of a Deficient Manipulator
229(1)
8.15 Inverse Motion Analysis of a Regular Manipulator Using the Detailed Formulation
230(3)
8.15.1 Inverse Velocity Solution
230(1)
8.15.2 Inverse Acceleration Solution
231(2)
9 Kinematic Analyses of Typical Serial Manipulators
233(108)
9.1 Puma Manipulator
233(17)
9.1.1 Kinematic Description According to the D-H Convention
234(1)
9.1.2 Forward Kinematics in the Position Domain
235(2)
9.1.3 Inverse Kinematics in the Position Domain
237(3)
9.1.4 Multiplicity Analysis
240(2)
9.1.5 Singularity Analysis in the Position Domain
242(2)
9.1.6 Forward Kinematics in the Velocity Domain
244(1)
9.1.7 Inverse Kinematics in the Velocity Domain
245(2)
9.1.8 Singularity Analysis in the Velocity Domain
247(3)
9.2 Stanford Manipulator
250(8)
9.2.1 Kinematic Description According to the D-H Convention
250(1)
9.2.2 Forward Kinematics in the Position Domain
251(2)
9.2.3 Inverse Kinematics in the Position Domain
253(1)
9.2.4 Multiplicity Analysis
254(1)
9.2.5 Singularity Analysis in the Position Domain
255(1)
9.2.6 Forward Kinematics in the Velocity Domain
255(1)
9.2.7 Inverse Kinematics in the Velocity Domain
256(1)
9.2.8 Singularity Analysis in the Velocity Domain
257(1)
9.3 Elbow Manipulator
258(15)
9.3.1 Kinematic Description According to the D-H Convention
259(1)
9.3.2 Forward Kinematics in the Position Domain
260(2)
9.3.3 Inverse Kinematics in the Position Domain
262(2)
9.3.4 Multiplicity Analysis
264(2)
9.3.5 Singularity Analysis in the Position Domain
266(3)
9.3.6 Forward Kinematics in the Velocity Domain
269(1)
9.3.7 Inverse Kinematics in the Velocity Domain
269(2)
9.3.8 Singularity Analysis in the Velocity Domain
271(2)
9.4 Scara Manipulator
273(8)
9.4.1 Kinematic Description According to the D-H Convention
273(1)
9.4.2 Forward Kinematics in the Position Domain
274(1)
9.4.3 Inverse Kinematics in the Position Domain
275(2)
9.4.4 Multiplicity Analysis
277(1)
9.4.5 Singularity Analysis in the Position Domain
278(1)
9.4.6 Forward Kinematics in the Velocity Domain
279(1)
9.4.7 Inverse Kinematics in the Velocity Domain
279(1)
9.4.8 Singularity Analysis in the Velocity Domain
280(1)
9.5 An RP2R3 Manipulator without an Analytical Solution
281(4)
9.5.1 Kinematic Description According to the D-H Convention
282(1)
9.5.2 Forward Kinematics in the Position Domain
282(1)
9.5.3 Inverse Kinematics in the Position Domain
283(2)
9.5 4 Multiplicity Analysis
285(5)
9.5.5 Singularity Analysis in the Position Domain
287(1)
9.5.6 Forward Kinematics in the Velocity Domain
287(1)
9.5.7 Inverse Kinematics in the Velocity Domain
287(2)
9.5.8 Singularity Analysis in the Velocity Domain
289(1)
9.6 An RPRPR2 Manipulator with an Uncustomary Analytical Solution
290(13)
9.6.1 Kinematic Description According to the D-H Convention
290(1)
9.6.2 Forward Kinematics in the Position Domain
291(2)
9.6.3 Inverse Kinematics in the Position Domain
293(4)
9.6.4 Multiplicity Analysis
297(1)
9.6.5 Singularity Analysis in the Position Domain
298(1)
9.6.6 Forward Kinematics in the Velocity Domain
298(1)
9.6.7 Inverse Kinematics in the Velocity Domain
299(2)
9.6.8 Singularity Analysis in the Velocity Domain
301(2)
9.7 A Deficient Puma Manipulator with Five Active Joints
303(10)
9.7.1 Kinematic Description According to the D-H Convention
303(1)
9.7.2 Forward Kinematics in the Position Domain
304(1)
9.7.3 Inverse Kinematics in the Position Domain
305(1)
9.7.3.1 Solution in the Case of Fully Specified Tip Point Location
305(2)
9.7.3.2 Solution in the Case of Fully Specified End-Effector Orientation
307(1)
9.7.4 Multiplicity Analysis in the Position Domain
307(1)
9.7.4.1 Analysis in the Case of Fully Specified Tip Point Location
307(1)
9.7.4.2 Analysis in the Case of Fully Specified End-Effector Orientation
308(1)
9.7.5 Singularity Analysis in the Position Domain
308(1)
9.7.5.1 Analysis in the Case of Fully Specified Tip Point Location
308(1)
9.7.5.2 Analysis in the Case of Fully Specified End-Effector Orientation
309(1)
9.7.6 Forward Kinematics in the Velocity Domain
310(1)
9.7.7 Inverse Kinematics in the Velocity Domain
310(1)
9.7.7 A Solution in the Case of Fully Specified Tip Point Velocity
310(1)
9.7.7.2 Solution in the Case of Fully Specified End-Effector Angular Velocity
311(1)
9.7.8 Singularity Analysis in the Velocity Domain
312(1)
9.7.8.1 Analysis in the Case of Fully Specified Tip Point Velocity
312(1)
9.7.8.2 Analysis in the Case of Fully Specified End-Effector Angular Velocity
313(1)
9.8 A Redundant Humanoid Manipulator with Eight Joints
313(28)
9.8.1 Kinematic Description According to the D-H Convention
313(2)
9.8.2 Forward Kinematics in the Position Domain
315(1)
9.8.3 Inverse Kinematics in the Position Domain
316(7)
9.8.4 Multiplicity Analysis
323(3)
9.8.5 Singularity Analysis in the Position Domain
326(2)
9.8.6 Forward Kinematics in the Velocity Domain
328(1)
9.8.7 Inverse Kinematics in the Velocity Domain
328(5)
9.8.8 Singularity Analysis in the Velocity Domain
333(2)
9.8.9 Consistency of the Inverse Kinematics in the Position and Velocity Domains
335(6)
10 Position and Velocity Analyses of Parallel Manipulators
341(82)
10.1 General Kinematic Features of Parallel Manipulators
343(4)
10.2 Position Equations of a Parallel Manipulator
347(4)
10.3 Forward Kinematics in the Position Domain
351(8)
10.4 Inverse Kinematics in the Position Domain
359(9)
10.5 Velocity Equations of a Parallel Manipulator
368(3)
10.6 Forward Kinematics in the Velocity Domain
371(6)
10.7 Inverse Kinematics in the Velocity Domain
377(7)
10.8 Stewart-Gough Platform as a 6UPS Spatial Parallel Manipulator
384(18)
10.8.1 Kinematic Description
384(2)
10.8.2 Position Equations
386(1)
10.8.3 Inverse Kinematics in the Position Domain
387(2)
10.8.4 Forward Kinematics in the Position Domain
389(7)
10.8.5 Velocity Equations
396(1)
10.8.6 Inverse Kinematics in the Velocity Domain
397(1)
10.8.7 Forward Kinematics in the Velocity Domain
398(4)
10.9 Delta Robot: A 3RS2S2 Spatial Parallel Manipulator
402(21)
10.9.1 Kinematic Description
402(2)
10.9.2 Position Equations
404(3)
10.9.3 Independent Kinematic Loops and the Associated Equations
407(3)
10.9.4 Inverse Kinematics in the Position Domain
410(2)
10.9.5 Forward Kinematics in the Position Domain
412(5)
10.9.6 Velocity Equations
417(1)
10.9.7 Inverse Kinematics in the Velocity Domain
418(2)
10.9.8 Forward Kinematics in the Velocity Domain
420(3)
Bibliography 423(2)
Index 425
M. KEMAL OZGOREN, PhD, is currently an Emeritus Professor at METU (Middle East Technical University), Ankara, Turkey. He was an active faculty member at the same university between 1976 and 2015. He received the BSc and MSc degrees from the Mechanical Engineering Department of METU in 1971 and 1972. He received the doctoral degree from the Mechanical Engineering Department of the Columbia University, USA, in 1976. His specific interest lies in the area of Spatial Kinematics but he is generally interested in the field of Kinematics, Dynamics, and Control of Mechanical Systems. In this field, his academic activities include teaching several courses, supervising numerous MSc and PhD theses, presenting papers in various national and international conferences, and publishing several archive journal papers. Additionally, he has acted as a Research Adviser for various National Defense Institutions and previously served as a Panel Member on the NATO-AGARD, Flight Mechanics Panel.
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