Parallel robots*

Herman Bruyninckx†

20 August, 2005

* This Chapter uses material from the Chapters on Serial robots and on Geometry.
† This text is part of The Robotics WEBook, http://www.roble.info. Copyright is held by the authors, who release the text and the figures under the open content WEBook license. You are invited to improve and extend this text.
1 Introduction
 1.1 Duality
 1.2 Kinematics
2 Parallel robot designs
 2.1 Design characteristics
 2.2 Nomenclature
3 Coordinate conventions and transformations
4 321 kinematic structure
 4.1 3-3 kinematic structure
 4.2 Non fully-parallel structure
5 Inverse position kinematics
6 Inverse force kinematics
 6.1 Partial wrenches for common “legs”
 6.2 Wrench basis for 321 structure
7 Inverse velocity kinematics
8 Forward position kinematics
 8.1 General parallel structure
 8.2 FPK by leg length error minimization
 8.3 Closed-form FPK for 321 structure
 8.4 Closed-form FPK: sensing redundancy
9 Forward velocity kinematics
 9.1 General parallel robots
 9.2 Closed-form FVK for 321 structure
10 Singularities
 10.1 Singularities for the 321 structure
11 Redundancy
12 Hybrid chains
13 Dynamics
14 Summary of serial/parallel dualities
References