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12 Result(s)
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Book
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Chapter
Forward Dynamics — Inertia Matrix Methods
Forward dynamics is the problem of finding the acceleration of a rigid-body system in response to given applied forces. It is used mainly for simulation; and it is sometimes called ‘direct dynamics’, or simply...
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Chapter
Introduction
Rigid-body dynamics is an old subject that has been rejuvenated and transformed by the computer. Today, we can find dynamics calculations in computer games, in animation and virtual-reality software, in simula...
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Chapter
Inverse Dynamics
Inverse dynamics is the problem of finding the forces required to produce a given acceleration in a rigid-body system. Inverse dynamics calculations are used in motion control systems, trajectory design and op...
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Chapter
Forward Dynamics — Propagation Methods
The forward dynamics problem presents us with two sets of unknowns: the joint accelerations and the joint constraint forces. It is usually not possible to solve for any of these unknowns locally at any one bod...
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Chapter
Accuracy and Efficiency
In theory, the algorithms presented in this book are all exact. However, the presence of round-off errors in the calculations ensures that the results are rarely so. Other sources of error include the use of n...
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Chapter
Closed Loop Systems
This chapter covers the forward and inverse dynamics of rigid-body systems containing kinematic loops. The presence of kinematic loops brings a new level of complexity to the dynamics problem: new formulations...
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Chapter
Contact and Impact
When two rigid bodies come into contact, they become subject to a contact constraint which says that the two bodies are not allowed to penetrate. If φ is a measure of the signed distance between them, meaning tha...
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Chapter
Dynamics of Rigid Body Systems
The purpose of a dynamics algorithm is to evaluate numerically an equation of motion; but, before we can evaluate it, we must first know what that equation is. This chapter introduces the equations of motion f...
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Chapter
Hybrid Dynamics and Other Topics
This chapter covers the following topics: hybrid dynamics, floating bases, gears and dynamic equivalence. Hybrid dynamics is a generalization of forward and inverse dynamics in which the forces are known at so...
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Chapter
Spatial Vector Algebra
Spatial vectors are 6D vectors that combine the linear and angular aspects of rigid-body motions and forces. They provide a compact notation for studying rigid-body dynamics, in which a single spatial vector c...
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Chapter
Modelling Rigid Body Systems
A rigid-body system is an assembly of component parts. Those components include rigid bodies, joints and various force elements. The joints are responsible for the kinematic constraints in the system, so we in...
