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Kinematics of mechanisms Download kinematics of mechanisms or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get kinematics of mechanisms book now. This site is like a library, Use search box in the widget to get ebook that you want. Analytical Kinematics Of Plane Motion Mechanisms Start Download Portable Document Format (PDF) and E-books. ☯ Full Synopsis: 'Spatial Mechanisms: Analysis and Synthesis comprises the study of the three-dimensional relative motion between the components of a machine. Each chapter in this book presents a concise, but thorough, fundamental. The simplest spatial closed chain is the RSSR linkage, which is often used in place of a planar four-bar linkage to allow for misalignment of the cranks (Fig. Figure 20.4 A spatial RSSR linkage. Another useful class of spatial mechanisms is produced by four hinges with concurrent axes that. To vertical kinematics have not been deeply explored with respect to downdraft-generated phenomena. Investigation of these complex, interconnected properties and processes related to high-impact phenomena requires more detailed analyses at finer spatial scales than reported in many studies of bulk thunderstorm properties.
Mechanisms And Machines Kinematics Dynamics And Synthesis
Author :Michael M. StanisicISBN :9781305177949
Planar Mechanism Kinematic Simulator
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MECHANISMS AND MACHINES: KINEMATICS, DYNAMICS, AND SYNTHESIS has been designed to serve as a core textbook for the mechanisms and machines course, targeting junior level mechanical engineering students. The book is written with the aim of providing a complete, yet concise, text that can be covered in a single-semester course. The primary goal of the text is to introduce students to the synthesis and analysis of planar mechanisms and machines, using a method well suited to computer programming, known as the Vector Loop Method. Author Michael Stanisic's approach of teaching synthesis first, and then going into analysis, will enable students to actually grasp the mathematics behind mechanism design. The book uses the vector loop method and kinematic coefficients throughout the text, and exhibits a seamless continuity in presentation that is a rare find in engineering texts. The multitude of examples in the book cover a large variety of problems and delineate an excellent problem solving methodology. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Mechanisms And Machines Kinematics Dynamics And Synthesis Si Edition
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MECHANISMS AND MACHINES: KINEMATICS, DYNAMICS, AND SYNTHESIS has been designed to serve as a core textbook for the mechanisms and machines course, targeting junior level mechanical engineering students. The book is written with the aim of providing a complete, yet concise, text that can be covered in a single-semester course. The primary goal of the text is to introduce students to the synthesis and analysis of planar mechanisms and machines, using a method well suited to computer programming, known as the Vector Loop Method. Author Michael Stanisic's approach of teaching synthesis first, and then going into analysis, will enable students to actually grasp the mathematics behind mechanism design. The book uses the vector loop method and kinematic coefficients throughout the text, and exhibits a seamless continuity in presentation that is a rare find in engineering texts. The multitude of examples in the book cover a large variety of problems and delineate an excellent problem solving methodology. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Mechanisms And Machines
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Design Of Machinery
Author :Robert L. NortonISBN :0071214968
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Design of Machinery continues the tradition of this best-selling book through its balanced coverage of analysis and design, and outstanding use of realistic engineering examples. Through its reader-friendly style of writing, clear exposition of complex topics, and emphasis on synthesis and design, the text succeeds in conveying the art of design as well as the use of modern tools needed for analysis of the kinematics and dynamics of machinery. Numerous two-color illustrations are used throughout to provide a visual approach to understanding mechanisms and machines. Analytical synthesis of linkages is covered, and cam design is given a more thorough, practical treatment than found in other texts. To provide an integrated look at the use of software tools for analysis and design, Design of Machinery includes a CD-ROM with a fully functioning version of MSC. Working Model 2D v. 5.2, and over 100 Working Model simulations for readers to work with. The CD-ROM also includes the author's updated, user-friendly programs; FOURBAR, FIVEBAR, SIXBAR, SLIDER, DYNACAM, ENGINE and MATRIX. The book's website offers instructor and student resources, a collection of MATLAB simulations, and 100 interactive Fundamentals of Engineering (FE) Exam questions on machine design, kinematics and machine dynamics. Book jacket.
Theory Of Mechanisms And Machines
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Intended to cater to the needs of undergraduate students in mechanical, production, and industrial engineering disciplines, this book provides a comprehensive coverage of the fundamentals of analysis and synthesis (kinematic and dynamic) of mechanisms and machines. It clearly describes the techniques needed to test the suitability of a mechanical system for a given task and to develop a mechanism or machine according to the given specifications. The text develops, in addition, a strong understanding of the kinematics of mechanisms and discusses various types of mechanisms such as cam-and-follower, gears, gear trains and gyroscope.
Kinematic Analysis And Synthesis Of Mechanisms
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This text/reference represents the first balanced treatment of graphical and analytical methods for kinematic analysis and synthesis of linkages (planar and spatial) and higher-pair mechanisms (cams and gears) in a single-volume format. A significant amount of excellent German literature in the field that previously was not available in English provides extra insight into the subject. Plenty of solved problems and exercise problems are included to sharpen your skills and demonstrate how theory is put into practice.
Kinematics And Dynamics Of Machinery
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Kinematics and Dynamics of Machinery teaches readers how to analyze the motion of machines and mechanisms. Coverage of a broad range of machines and mechanisms with practical applications given top consideration.Mechanisms and Machines. Motion in Machinery. Velocity Analysis of Mechanisms. Acceleration Analysis of Mechanisms. Cams. Spur Gears. Helical, Worm, and Bevel Gears. Drive Trains. Static-Force Analysis. Dynamic-Force Analysis. Synthesis. Introduction to Robotic Manipulators.
Mechanism And Machine Theory
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This book meets the requirements of undergraduate and postgraduate students pursuing courses in mechanical, production, electrical, metallurgical and aeronautical engineering. This self-contained text strikes a fine balance between conceptual clarity and practice problems, and focuses both on conventional graphical methods and emerging analytical approach in the treatment of subject matter. In keeping with technological advancement, the text gives detailed discussion on relatively recent areas of research such as function generation, path generation and mechanism synthesis using coupler curve, and number synthesis of kinematic chains. The text is fortified with fairly large number of solved examples and practice problems to further enhance the understanding of the otherwise complex concepts. Besides engineering students, those preparing for competitive examinations such as GATE and Indian Engineering Services (IES) will also find this book ideal for reference. KEY FEATURES Exhaustive treatment given to topics including gear drive and cam follower combination, analytical method of motion and conversion phenomenon. Simplified explanation of complex subject matter. Examples and exercises for clearer understanding of the concepts.
New Advances In Mechanisms Mechanical Transmissions And Robotics
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This volume presents the proceedings of the Joint International Conference of the XII International Conference on Mechanisms and Mechanical Transmissions (MTM) and the XXIII International Conference on Robotics (Robotics ’16), that was held in Aachen, Germany, October 26th-27th, 2016. It contains applications of mechanisms and transmissions in several modern technical fields such as mechatronics, biomechanics, machines, micromachines, robotics and apparatus. In connection with these fields, the work combines the theoretical results with experimental testing. The book presents reviewed papers developed by researchers specialized in mechanisms analysis and synthesis, dynamics of mechanisms and machines, mechanical transmissions, biomechanics, precision mechanics, mechatronics, micromechanisms and microactuators, computational and experimental methods, CAD in mechanism and machine design, mechanical design of robot architecture, parallel robots, mobile robots, micro and nano robots, sensors and actuators in robotics, intelligent control systems, biomedical engineering, teleoperation, haptics, and virtual reality.
Kinematics And Dynamics Of Machinery
Author :Robert L. NortonISBN :0071278524
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This book covers the kinematics and dynamics of machinery topics. It emphasizes the synthesis and design aspects and the use of computer-aided engineering. A sincere attempt has been made to convey the art of the design process to students in order to prepare them to cope with real engineering problems in practice. This book provides up-to-date methods and techniques for analysis and synthesis that take full advantage of the graphics microcomputer by emphasizing design as well as analysis. In addition, it details a more complete, modern, and thorough treatment of cam design than existing texts in print on the subject. The author’s website at www.designofmachinery.com has updates, the author’s computer programs and the author’s PowerPoint lectures exclusively for professors who adopt the book. Features Student-friendly computer programs written for the design and analysis of mechanisms and machines. Downloadable computer programs from website Unstructured, realistic design problems and solutions
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Table of Contents
4 Basic Kinematics of Constrained Rigid Bodies
4.1 Degrees of Freedom of a Rigid Body
4.1.1 Degrees of Freedom of a Rigid Body in a Plane
The degrees of freedom (DOF) of a rigid body is definedas the number of independent movements it has. Figure 4-1shows a rigid body in a plane. To determine the DOF of this bodywe must consider how many distinct ways the bar can be moved. Ina two dimensional plane such as this computer screen, there are 3 DOF.The bar can be translated along the x axis, translatedalong the y axis, and rotated about its centroid.
Figure 4-1 Degrees of freedom of a rigid body in a plane
4.1.2 Degrees of Freedom of a Rigid Body in Space
An unrestrained rigid body in space has six degrees of freedom:three translating motions along the x, y and zaxes and three rotary motions around the x, y andz axes respectively.
Figure 4-2 Degrees of freedom of a rigid body in space
Two or more rigid bodies in space are collectively called a rigidbody system. We can hinder the motion of these independent rigidbodies with kinematic constraints. Kinematicconstraints are constraints between rigid bodies that result inthe decrease of the degrees of freedom of rigid body system.
The term kinematic pairs actually refers tokinematic constraints between rigid bodies. The kinematic pairsare divided into lower pairs and higher pairs, depending on how the twobodies are in contact.
4.2.1 Lower Pairs in Planar Mechanisms
There are two kinds of lower pairs in planar mechanisms: revolute pairs and prismatic pairs.
A rigid body in a plane has only three independent motions -- twotranslational and one rotary -- so introducing either a revolute pairor a prismatic pair between two rigid bodies removes two degrees offreedom.
Figure 4-3 A planar revolute pair (R-pair)
Figure 4-4 A planar prismatic pair (P-pair)
4.2.2 Lower Pairs in Spatial Mechanisms
There are six kinds of lower pairs under the category of spatial mechanisms. The types are: spherical pair, plane pair,cylindrical pair, revolutepair, prismatic pair, and screw pair.
Figure 4-5 A spherical pair (S-pair)
A spherical pair keeps two spherical centers together. Tworigid bodies connected by this constraint will be able torotate relatively around x, y and z axes,but there will be no relative translation along any of theseaxes. Therefore, a spherical pair removes three degrees of freedom inspatial mechanism. DOF = 3.
Figure 4-6 A planar pair (E-pair)
A plane pair keeps the surfaces of two rigid bodies together.To visualize this, imagine a book lying on a table where is can movein any direction except off the table. Two rigid bodies connected bythis kind of pair will have two independent translational motions inthe plane, and a rotary motion around the axis that is perpendicularto the plane. Therefore, a plane pair removes three degrees offreedom in spatial mechanism. In our example, the book would not beable to raise off the table or to rotate into the table. DOF =3.
Figure 4-7 A cylindrical pair (C-pair)
A cylindrical pair keeps two axes of two rigid bodiesaligned. Two rigid bodies that are part of this kind of system willhave an independent translational motion along the axis and a relativerotary motion around the axis. Therefore, a cylindrical pair removesfour degrees of freedom from spatial mechanism. DOF = 2.
Figure 4-8 A revolute pair (R-pair)
A revolute pair keeps the axes of two rigid bodiestogether. Two rigid bodies constrained by a revolute pair have anindependent rotary motion around their common axis. Therefore, arevolute pair removes five degrees of freedom in spatialmechanism. DOF = 1.
Figure 4-9 A prismatic pair (P-pair)
A prismatic pair keeps two axes of two rigid bodies align andallow no relative rotation. Two rigid bodies constrained by this kindof constraint will be able to have an independent translational motionalong the axis. Therefore, a prismatic pair removes five degrees offreedom in spatial mechanism. DOF = 1.
Figure 4-10 A screw pair (H-pair)
The screw pair keeps two axes of two rigid bodies aligned andallows a relative screw motion. Two rigid bodies constrained by ascrew pair a motion which is a composition of a translational motionalong the axis and a corresponding rotary motion around the axis.Therefore, a screw pair removes five degrees of freedom in spatialmechanism.
4.3 Constrained Rigid Bodies
Rigid bodies and kinematic constraints are the basic components ofmechanisms. A constrained rigid body system can be a kinematic chain, a mechanism, a structure, or none of these.The influence of kinematic constraints in the motion of rigid bodieshas two intrinsic aspects, which are the geometrical and physicalaspects. In other words, we can analyze the motion of the constrainedrigid bodies from their geometrical relationships or using Newton's Second Law.
A mechanism is a constrained rigid body system in which one of thebodies is the frame. The degrees offreedom are important when considering a constrained rigid body systemthat is a mechanism. It is less crucial when the system is astructure or when it does not have definite motion.
Calculating the degrees of freedom of a rigid body system is straightforward. Any unconstrained rigid body has six degrees of freedom inspace and three degrees of freedom in a plane. Adding kinematicconstraints between rigid bodies will correspondingly decrease thedegrees of freedom of the rigid body system. We will discuss more onthis topic for planar mechanisms in the next section.
4.4 Degrees of Freedom of Planar Mechanisms
4.4.1 Gruebler's Equation
The definition of the degrees of freedom of a mechanismis the number of independent relative motions among the rigid bodies.For example, Figure 4-11 shows several cases of arigid body constrained by different kinds of pairs.
Figure 4-11 Rigid bodies constrained by different kinds of planar pairs
In Figure 4-11a, a rigid body is constrained by a revolute pair which allows only rotationalmovement around an axis. It has one degree of freedom, turning aroundpoint A. The two lost degrees of freedom are translational movementsalong the x and y axes. The only way the rigid body canmove is to rotate about the fixed point A.
In Figure 4-11b, a rigid body is constrained by a prismatic pair which allows onlytranslational motion. In two dimensions, it has one degree offreedom, translating along the x axis. In this example, thebody has lost the ability to rotate about any axis, and it cannot movealong the y axis.
In Figure 4-11c, a rigid body is constrained by a higher pair. It has two degrees offreedom: translating along the curved surface and turning about theinstantaneous contact point.
In general, a rigid body in a plane has three degrees of freedom.Kinematic pairs are constraints on rigid bodies that reduce thedegrees of freedom of a mechanism. Figure 4-11 shows the three kindsof pairs in planar mechanisms. Thesepairs reduce the number of the degreesof freedom. If we create a lower pair(Figure 4-11a,b), the degrees of freedom are reduced to 2. Similarly,if we create a higher pair (Figure4-11c), the degrees of freedom are reduced to 1.
Figure 4-12 Kinematic Pairs in Planar Mechanisms
Therefore, we can write the following equation:
(4-1)Where
- F = total degrees of freedom in the mechanism
- n = number of links (includingthe frame)
- l = number of lower pairs(one degree of freedom)
- h = number of higher pairs(two degrees of freedom)
This equation is also known as Gruebler's equation.
Example 1
Look at the transom above the door in Figure 4-13a. The opening andclosing mechanism is shown in Figure 4-13b. Let's calculate itsdegree of freedom.
Figure 4-13 Transom mechanism
n = 4 (link 1,3,3 and frame 4), l = 4 (at A, B, C, D), h = 0
(4-2)Note: D and E function as a same prismatic pair, so they only count as one lower pair.
Example 2
Calculate the degrees of freedom of the mechanisms shown in Figure 4-14b.Figure 4-14a is an application of the mechanism.
Figure 4-14 Dump truck
Example 3
Calculate the degrees of freedom of the mechanisms shown in Figure 4-15.
Figure 4-15 Degrees of freedom calculation
For the mechanism in Figure 4-15a
n = 6, l = 7, h = 0
(4-4)For the mechanism in Figure 4-15b
n = 4, l = 3, h = 2
(4-5)Kinematics Spatial Mechanisms Pdf File Size
Note: The rotation of the roller does not influence therelationship of the input and output motion of the mechanism. Hence,the freedom of the roller will not be considered; It is called apassive or redundant degree of freedom.Imagine that the roller is welded to link 2 when counting the degreesof freedom for the mechanism.
4.4.2 Kutzbach Criterion
The number of degrees of freedom of a mechanismis also called the mobility of the device. Themobility is the number of input parameters (usually pairvariables) that must be independently controlled to bring the deviceinto a particular position. The Kutzbach criterion,which is similar to Gruebler's equation,calculates the mobility.
In order to control a mechanism, the number of independent inputmotions must equal the number of degrees of freedom of the mechanism.For example, the transom in Figure 4-13ahas a single degree of freedom, so it needs one independent inputmotion to open or close the window. That is, you just push or pull rod 3to operate the window.
To see another example, the mechanism in Figure4-15a also has 1 degree of freedom. If an independent input isapplied to link 1 (e.g., a motor is mounted on joint A to drivelink 1), the mechanism will have the a prescribed motion.
4.5 Finite Transformation
Finite transformation is used to describe the motion of a point onrigid body and the motion of the rigid body itself.
4.5.1 Finite Planar Rotational Transformation
Figure 4-16 Point on a planar rigid body rotated through an angle
Suppose that a point P on a rigid body goes through a rotationdescribing a circular path from P1 toP2 around the origin of a coordinate system. We candescribe this motion with a rotation operatorR12:
(4-6)where
(4-7)4.5.2 Finite Planar TranslationalTransformation
Figure 4-17 Point on a planar rigid body translated through a distance
where
(4-9)4.5.3 Concatenation of Finite Planar Displacements
Figure 4-18 Concatenation of finite planar displacements in space
and
(4-11)Kinematics Spatial Mechanisms Pdf Files
We can concatenate these motions to get
(4-12)where D12 is the planar general displacement operator:
(4-13)4.5.4 Planar Rigid-Body Transformation
We have discussed various transformations to describe thedisplacements of a point on rigid body. Can these operators beapplied to the displacements of a system of points such as a rigidbody?
We used a 3 x 1 homogeneous column matrix to describe a vectorrepresenting a single point. A beneficial feature of the planar 3 x 3translational, rotational, and general displacement matrix operatorsis that they can easily be programmed on a computer to manipulate a 3x n matrix of n column vectors representing n points of a rigid body.Since the distance of each particle of a rigid body from every otherpoint of the rigid body is constant, the vectors locating each pointof a rigid body must undergo the same transformation when the rigidbody moves and the proper axis, angle, and/or translation is specifiedto represent its motion. (Sandor& Erdman 84). For example, the general planar transformationfor the three points A, B, C on a rigid body can be representedby
(4-14)4.5.5 Spatial Rotational Transformation
We can describe a spatial rotation operator for the rotationaltransformation of a point about an unit axis u passing through theorigin of the coordinate system. Suppose the rotational angle of the pointabout u is ,the rotation operator will be expressed by
(4-15)where
- ux, uy, uz are the othographicalprojection of the unit axis u on x, y, and z axes, respectively.
- s =sin
- c =cos
- v = 1 -cos
4.5.6 Spatial Translational Transformation
Suppose that a point P on a rigid body goes through atranslation describing a straight path from P1 toP2 with a change of coordinates of (x, y, z), we can describe thismotion with a translation operator T:
(4-16)4.5.7 Spatial Translation and Rotation Matrix for AxisThrough the Origin
Suppose a point P on a rigid body rotates with an angulardisplacement about an unit axis u passing through the origin ofthe coordinate system at first, and then followed by a translationDu along u. This composition of this rotationaltransformation and this translational transformation is a screwmotion. Its corresponding matrix operator, the screwoperator, is a concatenation of the translation operator in Equation 4-7 and the rotation operator in Equation 4-9.
4.6 Transformation Matrix Between Rigid Bodies
4.6.1 Transformation Matrix Between two ArbitrayRigid Bodies
For a system of rigid bodies, we can establish a local Cartesiancoordinate system for each rigid body. Transformation matrices areused to describe the relative motion between rigid bodies.
For example, two rigid bodies in a space each have local coordinatesystems x1y1z1 andx2y2z2. Let point P beattached to body 2 at location (x2, y2,z2) in body 2's local coordinate system. To find thelocation of P with respect to body 1's local coordinate system,we know that that the point x2y2z2can be obtained from x1y1z1 bycombining translation Lx1 along the x axis androtation z about zaxis. We can derive the transformation matrix as follows:
(4-18)If rigid body 1 is fixed as a frame, aglobal coordinate system can be created on this body. Therefore, theabove transformation can be used to map the local coordinates of apoint into the global coordinates.
4.6.2 Kinematic Constraints Between Two RigidBodies
The transformation matrix above is a specific example for twounconstrained rigid bodies. The transformation matrix depends on therelative position of the two rigid bodies. If we connect two rigidbodies with a kinematic constraint, theirdegrees of freedom will be decreased. In other words, their relativemotion will be specified in some extent.
Suppose we constrain the two rigid bodies above with a revolute pair as shown in Figure 4-19. We canstill write the transformation matrix in the same form as Equation 4-18.
Figure 4-19 Relative position of points on constrained bodies
The difference is that the Lx1 is a constantnow, because the revolute pair fixes the origin of coordinate systemx2y2z2 with respect to coordinate systemx1y1z1. However, the rotationzis still a variable. Therefore, kinematic constraints specify thetransformation matrix to some extent.
4.6.3 Denavit-Hartenberg Notation
Denavit-Hartenberg notation (Denavit & Hartenberg 55) iswidely used in the transformation of coordinate systems of linkages and robot mechanisms. It can beused to represent the transformation matrix between links as shown inthe Figure 4-20.
Figure 4-20 Denavit-Hartenberg Notation
The above transformation matrix can be denoted as T(ai,i, i, di)for convenience.
A linkage is composed of several constrained rigid bodies. Like amechanism, a linkage should have a frame. The matrix method can beused to derive the kinematic equations of the linkage. If all thelinks form a closed loop, the concatenation of all of thetransformation matrices will be an identity matrix. If the mechanismhas n links, we will have:
T12T23...T(n-1)n = I
Table of Contents
Complete Table of ContentsKinematics Spatial Mechanisms Pdf File Free
- 1 Introduction to Mechanisms
- 2 Mechanisms and Simple Machines
- 3 More on Machines and Mechanisms
- 4 Basic Kinematics of Constrained Rigid Bodies
- 4.1 Degrees of Freedom of a Rigid Body
- 4.1.1Degrees of Freedom of a Rigid Body in a Plane
- 4.1.2 Degrees of Freedom of a Rigid Body in Space
- 4.2 Kinematic Constraints
- 4.2.1 Lower Pairs in Planar Mechanisms
- 4.2.2 Lower Pairs in Spatial Mechanisms
- 4.3 Constrained Rigid Bodies
- 4.4 Degrees of Freedom of Planar Mechanisms
- 4.4.1 Gruebler's Equation
- 4.2.2 4.4.2 Kutzbach Criterion
- 4.5 4.5 Finite Transformation
- 4.5.1 Finite Planar Rotational Transformation
- 4.5.2 Finite Planar Translational Transformation
- 4.5.3 Concatenation of Finite Planar Displacements
- 4.5.4 Planar Rigid-Body Transformation
- 4.5.5 Spatial Rotational Transformation
- 4.5.6 Spatial Translational Transformation
- 4.5.7 Spatial Translation and Rotation Matrix for Axis Through the Origin
- 4.6 Transformation Matrix Between Rigid Bodies
- 4.6.1 Transformation Matrix Between two Arbitray Rigid Bodies
- 4.6.2 Kinematic Constraints Between Two Rigid Bodies
- 4.6.3 Denavit-Hartenberg Notation
- 4.6.4 Application of Transformation Matrices to Linkages
- 4.1 Degrees of Freedom of a Rigid Body
- 5 Planar Linkages
- 6 Cams
- 7 Gears
- 8 Other Mechanisms
- Index
- References