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## Über dieses Buch

This book represents the fifth part of a larger work dedicated to the structural synthesis of parallel robots. The originality of this work resides in the fact that it combines new formulae for mobility, connectivity, redundancy and overconstraints with evolutionary morphology in a unified structural synthesis approach that yields interesting and innovative solutions for parallel robotic manipulators.

This is the first book on robotics that presents solutions for coupled, decoupled, uncoupled, fully-isotropic and maximally regular robotic manipulators with Schönflies motions systematically generated by using the structural synthesis approach proposed in Part 1. Overconstrained non-redundant/overactuated/redundantly actuated solutions with simple/complex limbs are proposed. Many solutions are presented here for the first time in the literature. The author had to make a difficult and challenging choice between protecting these solutions through patents and releasing them directly into the public domain. The second option was adopted by publishing them in various recent scientific publications and above all in this book. In this way, the author hopes to contribute to a rapid and widespread implementation of these solutions in future industrial products.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
This book represents Part 5 of a larger work on the structural synthesis of parallel robots. The originality of this work resides in combining new formulae for the structural parameters and the evolutionary morphology in a unified approach of structural synthesis giving interesting innovative solutions for parallel robots. Part 1 [1] presented the methodology of structural synthesis and the systematisation of structural solutions of simple and complex limbs with two to six degrees of connectivity systematically generated by the structural synthesis approach. Part 2 [2] presented structural solutions of translational parallel robotic manipulators with two and three degrees of mobility. Part 3 [3] presented structural solutions of parallel robotic manipulators with planar motion of the moving platform. Part 4 [4] presented structural solutions of other parallel robotic manipulators with two and three degrees of freedom of the moving platform. Part 5 of this work focuses on the basic structural solutions of overconstrained parallel robotic manipulators with Schönflies motions of the moving platform.
Grigore Gogu

### Chapter 2. Fully-Parallel Topologies with Coupled Schönflies Motions

Abstract
In the general case, in a parallel robotic manipulator with coupled Schönflies motions each operational velocity depends on four actuated joint velocities $$v_{i} = v_{i} (\dot{q}_{1} ,\dot{q}_{2} ,\dot{q}_{3} ,\dot{q}_{3} ,\dot{q}_{4} )$$, i = 1, 2, 3 and $$\omega_{\delta } = \omega_{\delta } (\dot{q}_{1} ,\dot{q}_{2} ,\dot{q}_{3} ,\dot{q}_{4} )$$.
Grigore Gogu

### Chapter 3. Overactuated Topologies with Coupled Schönflies Motions

Abstract
In the overactuated parallel robotic manipulator with coupled Schönflies motions presented in this section each operational velocity depends on maximum three independent actuated joint velocities $$v_{1} = v_{1} (\dot{q}_{1} ,\dot{q}_{2} ,\dot{q}_{3} ),\;v_{2} = v_{2} (\dot{q}_{1} ,\dot{q}_{2} ,\dot{q}_{3} ),\;v_{3} = v_{3} (\dot{q}_{4} )$$ and $$\omega_{\delta } = \omega_{\delta } (\dot{q}_{1} ,\dot{q}_{2} ,\dot{q}_{3} )$$. In these topologies the operational velocity v 3 is uncoupled, but the Jacobian matrix in Eq. (1.​18) is not triangular and the parallel robot always has coupled motions.
Grigore Gogu

### Chapter 4. Fully-Parallel Topologies with Decoupled Schönflies Motions

Abstract
In the parallel robotic manipulators with decoupled Schönflies motions presented in this chapter each translational velocity of the moving platform depends on one actuated joint velocity $$v_{i} = v_{i} (\dot{q}_{i} )$$, i = 1, 2, 3 and the rotational velocity on two actuated joint velocities $$\omega_{\delta } = \omega_{\delta } (\dot{q}_{3} ,\dot{q}_{4} )$$. The Jacobian matrix in Eq. (1.18) is triangular and the parallel robot has decoupled motions.
Grigore Gogu

### Chapter 5. Topologies with Uncoupled Schönflies Motions

Abstract
In the parallel robotic manipulators with uncoupled Schönflies motions presented in this chapter each independent velocity of the moving platform depends on one actuated joint velocity $$v_{i} = v_{i} (\dot{q}_{i} )$$, i = 1, 2, 3 and $$\omega_{\delta } = \omega_{\delta } (\dot{q}_{4} )$$. The Jacobian matrix in Eq. (1.18) is diagonal and the parallel robot has uncoupled motions.
Grigore Gogu

### Chapter 6. Maximally Regular Topologies with Schönflies Motions

Abstract
Maximally regular parallel robotic manipulators with Schönflies motions are actuated by three linear and one rotating actuators and can have various degrees of over constraint. In these solutions, the four operational velocities are equal to their corresponding actuated joint velocities: $${\varvec{v}}_{1} = \dot{q}_{1}$$, $${\varvec{v}}_{2} = \dot{q}_{2}$$, $${\varvec{v}}_{3} = \dot{q}_{3}$$ and $${\varvec{\omega}}_{\delta } = \dot{q}_{4}$$. The Jacobian matrix in Eq. (1.​18) is the identity matrix. We call Isoglide4-T3R1 with Schönflies motions of the moving platform the parallel mechanisms of this family. The limbs can be simple or complex kinematic chains and the actuators can be mounted on the fixed base or on a moving link.
Grigore Gogu

### Backmatter

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