318:
522:
1105:
167:
1117:
20:
199:
Inverse kinematics specifies the end-effector location and computes the associated joint angles. For serial manipulators this requires solution of a set of polynomials obtained from the kinematics equations and yields multiple configurations for the chain. The case of a general 6R serial manipulator
275:
problem seeks the end-effector wrench associated with a given set of joint torques, and requires the inverse of the
Jacobian matrix. As in the case of inverse velocity analysis, at singular configurations this problem cannot be solved. However, near singularities small actuator torques result in a
142:
from specified values for the joint parameters. The reverse process that computes the joint parameters that achieve a specified position of the end-effector is known as inverse kinematics. The dimensions of the robot and its kinematics equations define the volume of space reachable by the robot,
180:
Forward kinematics specifies the joint parameters and computes the configuration of the chain. For serial manipulators this is achieved by direct substitution of the joint parameters into the forward kinematics equations for the serial chain. For parallel manipulators substitution of the joint
204:) yields sixteen different inverse kinematics solutions, which are solutions of a sixteenth degree polynomial. For parallel manipulators, the specification of the end-effector location simplifies the kinematics equations, which yields formulas for the joint parameters.
224:
shows that the
Jacobian also provides a relationship between joint torques and the resultant force and torque applied by the end-effector. Singular configurations of the robot are identified by studying its Jacobian.
233:
The robot
Jacobian results in a set of linear equations that relate the joint rates to the six-vector formed from the angular and linear velocity of the end-effector, known as a
511:
248:. It can happen that the robot is in a configuration where the Jacobian does not have an inverse. These are termed singular configurations of the robot.
154:. Other types of systems with specialized kinematics equations are air, land, and submersible mobile robots, hyper-redundant, or snake, robots and
317:
1090:
850:
372:
771:
443:
213:
766:
44:
1042:
916:
119:
A fundamental tool in robot kinematics is the kinematics equations of the kinematic chains that form the robot. These
860:
123:
are used to map the joint parameters to the configuration of the robot system. Kinematics equations are also used in
410:
1080:
476:
1143:
1068:
298:
717:
712:
244:
problem seeks the joint rates that provide a specified end-effector twist. This is solved by inverting the
364:
Robot manipulators: mathematics, programming, and control : the computer control of robot manipulators
911:
436:
67:
1022:
876:
486:
265:
77:
studies the relationship between the dimensions and connectivity of kinematic chains and the position,
972:
896:
661:
621:
471:
331:
277:
234:
151:
1121:
1063:
926:
626:
466:
120:
400:
John J. Craig, 2004, Introduction to
Robotics: Mechanics and Control (3rd Edition), Prentice-Hall.
50:
that form the structure of robotic systems. The emphasis on geometry means that the links of the
1032:
1007:
997:
962:
906:
886:
833:
806:
744:
656:
590:
491:
194:
175:
147:
139:
128:
114:
85:
of each of the links in the robotic system, in order to plan and control movement and to compute
1109:
1073:
1002:
931:
818:
604:
506:
481:
429:
368:
260:
yields a set of linear equations that relate the resultant force-torque six vector, called a
1058:
936:
921:
796:
788:
707:
666:
651:
599:
501:
341:
217:
102:
967:
952:
855:
845:
837:
702:
575:
553:
543:
289:
245:
47:
264:, that acts on the end-effector to the joint torques of the robot. If the end-effector
1085:
901:
891:
813:
756:
697:
636:
631:
616:
548:
521:
323:
201:
155:
59:
1137:
1037:
992:
676:
671:
646:
641:
170:
Forward kinematics of an over-actuated planar parallel manipulator done with MeKin2D.
801:
776:
761:
734:
724:
585:
496:
336:
261:
257:
221:
124:
82:
55:
276:
large end-effector wrench. Thus near singularity configurations robots have large
166:
362:
823:
749:
739:
729:
692:
609:
570:
101:
properties, motion, and the associated forces and torques is studied as part of
24:
313:
182:
74:
987:
881:
580:
181:
parameters into the kinematics equations requires solution of the a set of
146:
There are two broad classes of robots and associated kinematics equations:
1027:
977:
452:
86:
78:
63:
40:
32:
957:
538:
98:
237:. Specifying the joint rates yields the end-effector twist directly.
1012:
563:
558:
185:
constraints to determine the set of possible end-effector locations.
90:
19:
16:
Geometric analysis of multi-DoF kinematic chains that model a robot
982:
530:
165:
135:
51:
18:
1017:
94:
425:
268:
is known, then a direct calculation yields the joint torques.
216:
of the robot, which relates the joint rates to the linear and
421:
212:
The time derivative of the kinematics equations yields the
134:
Forward kinematics uses the kinematic equations of a
1051:
945:
869:
832:
787:
685:
529:
459:
306:, as well as the kinematic synthesis of robots.
437:
8:
444:
430:
422:
389:Introduction to Theoretical Kinematics,
367:. MIT Press, Cambridge, Massachusetts.
353:
220:of the end-effector. The principle of
851:Simultaneous localization and mapping
7:
391:MIT Press, Cambridge, Massachusetts.
14:
288:Robot kinematics also deals with
1115:
1104:
1103:
520:
316:
43:to the study of the movement of
1116:
138:to compute the position of the
409:J. M. McCarthy and G. S. Soh,
1:
412:Geometric Design of Linkages,
62:are assumed to provide pure
861:Vision-guided robot systems
415:2nd Edition, Springer 2010.
131:of articulated characters.
93:. The relationship between
1160:
1081:Technological unemployment
192:
173:
112:
1099:
1069:Workplace robotics safety
518:
200:(a serial chain with six
143:known as its workspace.
917:Human–robot interaction
45:multi-degree of freedom
387:J. M. McCarthy, 1990,
361:Paul, Richard (1981).
171:
28:
23:Inverse kinematics of
1023:Starship Technologies
294:singularity avoidance
252:Static force analysis
169:
152:parallel manipulators
113:Further information:
22:
973:Energid Technologies
332:Robotics conventions
278:mechanical advantage
127:of the skeleton and
121:non-linear equations
1064:Powered exoskeleton
304:collision avoidance
229:Velocity kinematics
148:serial manipulators
109:Kinematic equations
1033:Universal Robotics
1008:Intuitive Surgical
998:Harvest Automation
963:Barrett Technology
745:Robotic spacecraft
591:Audio-Animatronics
195:Inverse kinematics
189:Inverse kinematics
176:Forward kinematics
172:
162:Forward kinematics
129:computer animation
115:Kinematic equation
29:
27:done with MeKin2D.
1131:
1130:
1074:Robotic tech vest
1003:Honeybee Robotics
819:Electric unicycle
772:remotely-operated
374:978-0-262-16082-7
256:The principle of
1151:
1144:Robot kinematics
1119:
1118:
1107:
1106:
1091:Fictional robots
1059:Critique of work
708:Unmanned vehicle
524:
446:
439:
432:
423:
416:
407:
401:
398:
392:
385:
379:
378:
358:
342:Robot locomotion
326:
321:
320:
242:inverse velocity
218:angular velocity
48:kinematic chains
37:robot kinematics
1159:
1158:
1154:
1153:
1152:
1150:
1149:
1148:
1134:
1133:
1132:
1127:
1095:
1047:
968:Boston Dynamics
953:Amazon Robotics
941:
865:
856:Visual odometry
846:Motion planning
828:
783:
703:Continuum robot
686:Classifications
681:
544:Anthropomorphic
525:
516:
512:AI competitions
455:
450:
420:
419:
408:
404:
399:
395:
386:
382:
375:
360:
359:
355:
350:
322:
315:
312:
290:motion planning
286:
284:Fields of study
273:inverse statics
254:
246:Jacobian matrix
231:
210:
202:revolute joints
197:
191:
178:
164:
156:humanoid robots
117:
111:
54:are modeled as
17:
12:
11:
5:
1157:
1155:
1147:
1146:
1136:
1135:
1129:
1128:
1126:
1125:
1113:
1100:
1097:
1096:
1094:
1093:
1088:
1086:Terrainability
1083:
1078:
1077:
1076:
1066:
1061:
1055:
1053:
1049:
1048:
1046:
1045:
1040:
1035:
1030:
1025:
1020:
1015:
1010:
1005:
1000:
995:
990:
985:
980:
975:
970:
965:
960:
955:
949:
947:
943:
942:
940:
939:
934:
929:
924:
919:
914:
909:
904:
899:
894:
889:
884:
879:
873:
871:
867:
866:
864:
863:
858:
853:
848:
842:
840:
830:
829:
827:
826:
821:
816:
811:
810:
809:
799:
793:
791:
785:
784:
782:
781:
780:
779:
774:
764:
759:
754:
753:
752:
742:
737:
732:
727:
722:
721:
720:
715:
705:
700:
698:Cloud robotics
695:
689:
687:
683:
682:
680:
679:
674:
669:
664:
659:
654:
649:
644:
639:
634:
629:
624:
619:
614:
613:
612:
602:
597:
596:
595:
594:
593:
578:
573:
568:
567:
566:
561:
556:
551:
541:
535:
533:
527:
526:
519:
517:
515:
514:
509:
504:
499:
494:
489:
484:
479:
474:
469:
463:
461:
457:
456:
451:
449:
448:
441:
434:
426:
418:
417:
402:
393:
380:
373:
352:
351:
349:
346:
345:
344:
339:
334:
328:
327:
324:Physics portal
311:
308:
285:
282:
253:
250:
230:
227:
209:
208:Robot Jacobian
206:
193:Main article:
190:
187:
174:Main article:
163:
160:
110:
107:
103:robot dynamics
15:
13:
10:
9:
6:
4:
3:
2:
1156:
1145:
1142:
1141:
1139:
1124:
1123:
1114:
1112:
1111:
1102:
1101:
1098:
1092:
1089:
1087:
1084:
1082:
1079:
1075:
1072:
1071:
1070:
1067:
1065:
1062:
1060:
1057:
1056:
1054:
1050:
1044:
1041:
1039:
1038:Wolf Robotics
1036:
1034:
1031:
1029:
1026:
1024:
1021:
1019:
1016:
1014:
1011:
1009:
1006:
1004:
1001:
999:
996:
994:
993:Foster-Miller
991:
989:
986:
984:
981:
979:
976:
974:
971:
969:
966:
964:
961:
959:
956:
954:
951:
950:
948:
944:
938:
935:
933:
930:
928:
925:
923:
920:
918:
915:
913:
912:Developmental
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
883:
880:
878:
875:
874:
872:
868:
862:
859:
857:
854:
852:
849:
847:
844:
843:
841:
839:
835:
831:
825:
822:
820:
817:
815:
812:
808:
805:
804:
803:
800:
798:
795:
794:
792:
790:
786:
778:
775:
773:
770:
769:
768:
765:
763:
760:
758:
755:
751:
748:
747:
746:
743:
741:
738:
736:
733:
731:
728:
726:
723:
719:
716:
714:
711:
710:
709:
706:
704:
701:
699:
696:
694:
691:
690:
688:
684:
678:
677:Soft robotics
675:
673:
672:BEAM robotics
670:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
627:Entertainment
625:
623:
620:
618:
615:
611:
608:
607:
606:
603:
601:
598:
592:
589:
588:
587:
584:
583:
582:
579:
577:
574:
572:
569:
565:
562:
560:
557:
555:
552:
550:
547:
546:
545:
542:
540:
537:
536:
534:
532:
528:
523:
513:
510:
508:
505:
503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
475:
473:
470:
468:
465:
464:
462:
460:Main articles
458:
454:
447:
442:
440:
435:
433:
428:
427:
424:
414:
413:
406:
403:
397:
394:
390:
384:
381:
376:
370:
366:
365:
357:
354:
347:
343:
340:
338:
335:
333:
330:
329:
325:
319:
314:
309:
307:
305:
301:
300:
295:
291:
283:
281:
279:
274:
269:
267:
263:
259:
251:
249:
247:
243:
238:
236:
228:
226:
223:
219:
215:
207:
205:
203:
196:
188:
186:
184:
177:
168:
161:
159:
157:
153:
149:
144:
141:
137:
132:
130:
126:
122:
116:
108:
106:
104:
100:
96:
92:
88:
84:
80:
76:
71:
69:
65:
61:
57:
53:
49:
46:
42:
38:
34:
26:
21:
1120:
1108:
877:Evolutionary
824:Robotic fins
777:Robotic fish
762:Telerobotics
735:Nanorobotics
725:Mobile robot
662:Food service
657:Agricultural
507:Competitions
492:Hall of Fame
411:
405:
396:
388:
383:
363:
356:
337:Mobile robot
303:
297:
293:
287:
272:
270:
258:virtual work
255:
241:
239:
232:
222:virtual work
211:
198:
179:
145:
140:end-effector
133:
125:biomechanics
118:
83:acceleration
72:
56:rigid bodies
36:
30:
897:Open-source
750:Space probe
740:Necrobotics
730:Microbotics
693:Biorobotics
622:Educational
605:Articulated
586:Animatronic
571:Claytronics
89:forces and
68:translation
25:SCARA robot
937:Ubiquitous
927:Perceptual
834:Navigation
789:Locomotion
767:Underwater
652:Disability
600:Industrial
348:References
299:redundancy
183:polynomial
75:kinematics
988:Figure AI
946:Companies
922:Paradigms
907:Adaptable
887:Simulator
581:Automaton
576:Companion
487:Geography
1138:Category
1110:Category
1028:Symbotic
978:FarmWise
932:Situated
902:Software
870:Research
814:Climbing
637:Military
632:Juggling
617:Domestic
549:Humanoid
472:Glossary
453:Robotics
310:See also
214:Jacobian
87:actuator
79:velocity
64:rotation
58:and its
41:geometry
39:applies
33:robotics
1122:Outline
1052:Related
1043:Yaskawa
958:Anybots
838:mapping
807:Hexapod
802:Walking
647:Service
642:Medical
554:Android
539:Aerobot
482:History
467:Outline
99:inertia
91:torques
1013:IRobot
797:Tracks
718:ground
713:aerial
667:Retail
564:Gynoid
559:Cyborg
497:Ethics
371:
266:wrench
262:wrench
73:Robot
60:joints
983:FANUC
892:Suite
757:Swarm
531:Types
477:Index
235:twist
136:robot
52:robot
1018:KUKA
882:Kits
836:and
502:Laws
369:ISBN
271:The
240:The
150:and
105:.
97:and
95:mass
81:and
610:arm
66:or
31:In
1140::
302:,
296:,
292:,
280:.
158:.
70:.
35:,
445:e
438:t
431:v
377:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
