Parallel Robots

by Merlet, Jean-Pierre

• ISBN13: 9780792363088
• ISBN10: 0792363086
• Format: Hardcover
• Copyright: 2000-07-01
• Publisher: Kluwer Academic Pub

Summary

Parallel robots are closed-loop mechanisms presenting very good performances in terms of accuracy, rigidity and ability to manipulate large loads. Parallel robots have been used in a large number of applications ranging from astronomy to flight simulators and are becoming increasingly popular in the field of machine-tool industry. This book presents a complete synthesis of the latest results on the possible mechanical architectures, analysis and synthesis of this type of mechanism. It is intended to be used by students (with over 100 exercises and numerous Internet addresses), researchers (with over 500 references and anonymous ftp access to the code of some algorithms presented in this book) and engineers (for which practical results and applications are presented).

Table of Contents

Preface	xiii
Notation	xv
Introduction	1	(14)
Characteristics of classical robots	1	(3)
Other types of architecture	4	(4)
Needs for robotics	8	(1)
Parallel robots: definition	8	(4)
Generalized parallel manipulators: definition	9	(1)
Parallel manipulators	9	(1)
Fully parallel manipulators	9	(1)
Fully parallel manipulators: analysis	10	(1)
Planar robots	10	(1)
General case	11	(1)
Contents	12	(1)
Exercises	13	(2)
Architectures	15	(50)
Introduction	15	(1)
Planar robots	15	(3)
2 dof manipulators	15	(2)
3 dof manipulators	17	(1)
Spatial motion robots	18	(32)
Joints	19	(1)
Actuators	19	(1)
Classification of parallel robots	20	(1)
Synthesis of architectures	21	(1)
Generator combinations and intersections	21	(1)
Motion group generator	22	(1)
3 dof manipulators	22	(1)
Translation manipulators	23	(4)
Orientation manipulators	27	(3)
Complex degrees of freedom manipulators	30	(4)
4 dof manipulators	34	(1)
5 dof manipulators	34	(2)
6 dof manipulators	36	(1)
RRPS chain robot	36	(4)
PRRS chain robots	40	(2)
RRRS chain robots	42	(1)
Exotic chain robots	43	(5)
Decoupled robots	48	(2)
Articulated truss	50	(2)
Examples of applications	52	(9)
Spatial applications	52	(2)
Medical applications	54	(1)
Industrial applications	54	(2)
Joysticks	56	(1)
Simulators	57	(2)
Special applications	59	(2)
Notion of standard manipulators	61	(1)
Exercises	62	(3)
Jacobian and inverse kinematics	65	(26)
Inverse kinematics	65	(9)
General method	65	(1)
Planar manipulators	66	(1)
RRPS manipulators	67	(1)
PRRS manipulators	68	(1)
RRRS manipulators	69	(1)
Spherical manipulators	70	(1)
Extrema of the articular coordinates	71	(1)
Extrema for a cartesian box	71	(1)
Extrema for a sphere	72	(1)
Extrema for any space	72	(1)
Exact and approximate computation	73	(1)
Inverse jacobian matrix	74	(8)
Euler angles inverse jacobian	75	(1)
Example: RRPS manipulators	75	(1)
Inverse kinematic jacobian	76	(1)
Example: RRPS manipulators	77	(1)
Example: PRRS manipulators	78	(1)
Example: RRRS manipulators	79	(1)
Other example	79	(1)
Isotropy	80	(2)
Jacobian matrix	82	(1)
Direct calculation of the Jacobian	82	(1)
Jacobian matrix and intrnal sensors	83	(2)
Practical examples	84	(1)
Calibration	85	(3)
Exercises	88	(3)
Direct kinematics	91	(58)
Planar mechanism	91	(7)
The 4-bar mechanism	91	(1)
Coupler curve and circularity	92	(1)
Direct kinematics of the 3-RPR robot	93	(1)
Assembly modes	94	(1)
Polynomial direct kinematics	94	(2)
Particular cases	96	(1)
Other planar robots	97	(1)
Mechanisms for translations in space	98	(1)
Spherical mechanisms	98	(2)
6 degrees of freedom mechanisms	100	(19)
Example of analysis: the TSSM	100	(1)
Upper bound on the number of assembly modes	100	(2)
Polynomial formulation	102	(2)
Example of TSSM with 16 assembly modes	104	(2)
Analysis of other space mechanisms	106	(1)
MSSM	107	(1)
Active wrist	108	(1)
Stewart platform	109	(1)
3 degrees of freedom wrist	110	(3)
Main results	113	(1)
6-5 manipulators	113	(1)
6-4 manipulators	114	(1)
6-3 manipulators	115	(1)
5-5 manipulators	115	(1)
5-4 manipulators	115	(2)
4-4 manipulators	117	(1)
Manipulators with 5 aligned points	118	(1)
Manipulators PPP-3S,PRR-3S,PPR-3S	118	(1)
Nair systematic method	119	(7)
Principle of the method	119	(1)
The linear system	120	(1)
Closure equations	121	(1)
Resolution	121	(1)
Example: wrist with 3 degrees of freedom	122	(2)
Results of Nair's method	124	(1)
9 link manipulators	124	(1)
7 and 8 link manipulators	125	(1)
R-R manipulators	125	(1)
Conclusion	126	(1)
Case of the general robot	126	(4)
The SSM	126	(1)
Maximum number of assembly modes	126	(1)
Determination of the solutions	127	(1)
General robots	128	(1)
Maximum number of assembly modes	128	(1)
Determination of the solutions	128	(2)
Summary of results and conclusion	130	(3)
Fast numerical methods	133	(7)
Iterative methods	133	(4)
Methods efficiency and computation time	137	(1)
Convergence of the iterative methods	137	(3)
Drawbacks of iterative methods and real-time issues	140	(1)
Direct kinematics with extra sensors	140	(4)
Type and location of the extra sensors	141	(1)
Maximal number of sensors	141	(1)
Addition of angular sensors	142	(1)
Addition of linear sensors	142	(1)
Relationship between sensors accuracy and pose accuracy	142	(2)
Conclusions	144	(1)
Exercises	145	(4)
Singular configurations	149	(34)
Introduction	149	(2)
Singularities and velocity	149	(1)
Singularities and statics	150	(1)
Singularities and kinematics	150	(1)
State of the art	151	(1)
Grassmann geometry	152	(18)
Variety and geometry	153	(2)
Principle governing the search of singularities	155	(1)
Analytical examples	155	(1)
Planar manipulator	155	(2)
MSSM	157	(9)
Analysis of other spatial manipulators	166	(2)
TSSM	168	(1)
3 dof wrist	168	(2)
INRIA active wrist	170	(1)
Degrees of freedom associated with singularities	170	(4)
Example: the MSSM	171	(1)
Type 3d configuration	171	(1)
Type 5a configuration	172	(2)
Type 5b configuration	174	(1)
Manipulability and condition number	174	(3)
Practical search for singularities	177	(3)
Semi-jacobian method	178	(1)
Singularity in a cartesian box	178	(2)
Singularities in an articular workspace	180	(1)
Mechanisms in permanent singularity	180	(1)
Singularity-free path-planning	180	(1)
Exercises	181	(2)
Workspace	183	(50)
Workspace limits and representation	183	(5)
The different types of workspaces	183	(1)
State of the art	184	(4)
Calculation of the constant orientation workspace	188	(1)
Planar manipulator	189	(10)
Constant orientation workspace	189	(1)
Articular coordinates limits	190	(1)
Mechanical limits on the passive joints	190	(1)
Orientation workspace	191	(1)
Dextrous workspace	192	(1)
Maximal workspace	192	(4)
Inclusive orientation workspace	196	(1)
Total orientation workspace	197	(2)
6 dof manipulators	199	(19)
Cross-sections of the constant orientation workspace	199	(2)
3D constant orientation workspace	201	(2)
Workspace area and volume	203	(1)
Mechanical limits on the joints	204	(5)
Interference between links	209	(1)
Orientation workspace	210	(2)
Dextrous workspace	212	(2)
Maximal workspace	214	(2)
Comparison between architectures	216	(2)
Trajectory checking	218	(6)
Constant orientation trajectory	218	(1)
Limits on the link lengths	219	(1)
Mechanical limits on the joints	220	(1)
Computation time	220	(2)
Non constant orientation trajectory	222	(1)
Articular coordinates limits	222	(1)
Computation time and example	223	(1)
Path-planning	224	(6)
Introduction	224	(1)
Path-planning in a plane	224	(1)
Path-Planning with tiling	224	(1)
Path-planning with visibility graph	225	(1)
Path-planning in space with tiling	226	(1)
Path-planning for planar robots	227	(3)
Exercises	230	(3)
Velocity and Acceleration	233	(14)
Relations between the articular velocities and the generalized velocities	233	(1)
Determination of the articular velocities	233	(1)
Determination of the twist	233	(1)
Extrema of the generalized velocities	234	(5)
Extrema of the generalized velocities in a pose	234	(2)
Minimum of the cartesian velocity in a translation workspace	236	(3)
Extrema of the articular velocities in a translation workspace	239	(4)
Particular case	241	(1)
Determination of the motion of the passive joints	242	(1)
Accelerations	243	(1)
General robot	243	(1)
Active wrist	244	(1)
Conclusion	244	(1)
Exercises	245	(2)
Static analysis	247	(22)
Relations between generalized and articular forces	247	(1)
Fundamental relations	247	(1)
Determination of the generalized forces	247	(1)
Determination of the articular forces	247	(1)
Articular forces and maximal generalized forces	248	(7)
Maximal articular forces in a pose	248	(1)
Maximal articular forces in a translation workspace	249	(1)
Extrema on a line segment	250	(1)
Extrema for an horizontal rectangle	251	(1)
Extrema for a cartesian box	252	(1)
Maximal generalized forces in a pose	253	(1)
Maximal generalized forces in the workspace	254	(1)
Parallel robots as force sensors	255	(1)
Stiffness and compliance	256	(8)
Stiffness matrix of a parallel robot	256	(1)
Elastic model	256	(2)
Beam model	258	(1)
Passive compliance	258	(1)
Stiffness maps	259	(1)
Iso-stiffness maps	260	(1)
Iso-stiffness of the general robot	260	(3)
Iso-stiffness of the active wrist	263	(1)
Extrema of the stiffnesses in a workspace	264	(2)
Extrema on a line segment	264	(1)
Extrema on a rectangle	264	(1)
Extrema in a cartesian box	265	(1)
Balancing	266	(1)
Exercises	266	(3)
Dynamics	269	(14)
Introduction	269	(2)
MSSM inverse dynamics	271	(2)
SSM dynamics	273	(4)
Hypothesis and notation	273	(1)
Algorithm principle	274	(3)
Active wrist dynamics	277	(1)
Computation time	278	(1)
Examples	278	(3)
Inverse dynamics	279	(1)
Direct dynamics	279	(2)
Exercises	281	(2)
Design	283	(18)
Introduction	283	(4)
Design method	287	(13)
Reduction of the parameters	288	(1)
Restriction of the search space	289	(1)
Restriction via the workspace	289	(2)
Restriction via the articular velocities	291	(2)
Search for the optimal robot	293	(3)
Design examples	296	(1)
HFM2 robot	296	(2)
HDM1 robot	298	(2)
Exercises	300	(1)
Conclusion	301	(4)
WEB adresses	305	(4)
Index	309	(18)
References	327