Rigid Body Kinematics and C++ CodePresented here is an integrated approach - perhaps the first in its class - of advanced Rigid Body Kinematics with the object-oriented C++ code that implements the rigid body objects and brings them to life. Thinking in terms of objects is the natural way of thinking. The concept of object has existed in Science for centuries. More recently, objects were introduced in Computation, and object-oriented programming languages were created. Yet the concept of object is not routinely used when teaching Science, and the idea that objects can come alive in a computer has not yet been fully exploited.This book is Volume 2 of the multi-volume series "Articulated Robot Mechanics and C++ Code". Volume 1 is "Vectors, Matrices and C++ Code", published in 2004. Volumes to be published are "Articulated Robot Dynamics and C++ Code", and "Articulated Robot Control and C++ Code". More volumes may be added in the future.This book integrates advanced rigid body Kinematics with object-oriented concepts and the actual code implementing them. It is both a textbook and a software release, complete with software documentation and the mathematical background that supports the code. The source code is included by download and readers can use it for their own programming. The reader will need a basic knowledge of Physics, particularly Mechanics, and Algebra and Trigonometry. Familiarity with C++ is not required because a course on C++ is included in Volume 1. You should read this book if you are a developer who needs an advanced background in rigid body Kinematics, a student of Physics or Engineering who needs to learn C++, a scientist who needs to write advanced code but can't waste time developing the basics, or you just need ready-to-use C++ source code for your project. |
Contents
| 3 | |
| 17 | |
| 31 | |
| 49 | |
| 57 | |
Part II Code Documentation | 71 |
C++ Code for Rigid Body Kinematics | 73 |
Specific Coordinates | 77 |
Graphs | 179 |
Mechanical | 319 |
Bibliography and Index | 345 |
Common terms and phrases
0-based index AFS.F angular velocity WFS,F array of doubles axis Body object bool public breadth-first search Calculates matrix column vector connected component const CSVector const Vector3 constant CSVector object contain the resulting contains the given coordinate system graph Creates a report CSEdge CSVertex object current values EDGE object equation Euler angles Euler parameters expressed in system GDot given vector int public integer kinematic number of edges number of orientational object that contains omega_FSF open path ordered by rows orientation matrix AFS,F orientational specific coordinates orientational specific velocities orthogonal matrix PMatrix object PPathOpen<VERTEX protected Public constructor reference direction relative to system result by argument resulting matrix Return A reference Return The integer Return true returned by argument Returns a pointer Returns the number returns the result rigid body rotation sin(v Str object system F system S relative translational specific coordinates unit vectors vertex Virtual destructor void public WFS,S ZYX convention
Popular passages
Page 19 - The distance d(u, v} between two vertices u and v is the length of the shortest path connecting them. Given a vertex n, the largest distance between u and any other vertex of the graph is called the eccentricity e(u) of the vertex u. The largest eccentricity of any vertex in a graph is the diameter of the graph. A peripheral vertex is one for which the eccentricity is equal to the diameter of the graph. Algorithms for graphs associated with coordinate systems require a "starting" vertex having a...
Page 18 - V||E|1/2) time, where | V| is the number of vertices and \E\ is the number of edges [21].
Page 266 - Trees are normally drawn upside down, with the root at the top and the leaves at the bottom.
Page 20 - T = (V,E') c++ is a subgraph which is a tree and contains all the vertices of G. A spanning tree can be obtained by searching the graph and breaking cycles by deleting edges without disconnecting the graph. A convenient procedure for doing this is breadth-first search 2.2.1.
Page 19 - G, the distance d(u, v) between two vertices u and v is the length (number of edges) of the shortest path between them.
Page 20 - A graph is connected if every pair of vertices is connected by a path. A component is a connected subgraph G, c^ G that is maximal with respect to the inclusion of edges, ie if G...
Page 6 - A square matrix is said to be orthogonal, if its transpose is equal to its inverse.
Page 189 - The integer 0-based graph index of a vertex of the graph in the range 0 to n — 1, where n is the number of vertices of the graph.
Page 5 - Besides, U can be written U = D'U', where D' is diagonal with positive diagonal elements and U' is upper triangular with unit diagonal.