2668:
3652:
1914:
2663:{\displaystyle {\begin{pmatrix}P_{x}\\P_{y}\\d_{A}\\d_{B}\end{pmatrix}}={\frac {1}{\sin \left(\tau _{A}-\tau _{B}\right)}}{\begin{pmatrix}\left(B_{y}^{m}-A_{y}^{m}\right)\sin \tau _{A}\sin \tau _{B}+B_{x}^{m}\sin \tau _{A}\cos \tau _{B}-A_{x}^{m}\cos \tau _{A}\sin \tau _{B}\\\left(A_{x}^{m}-B_{x}^{m}\right)\cos \tau _{A}\cos \tau _{B}+A_{y}^{m}\sin \tau _{A}\cos \tau _{B}-B_{y}^{m}\cos \tau _{A}\sin \tau _{B}\\\left(B_{x}^{m}-A_{x}^{m}\right)\cos \tau _{B}+\left(B_{y}^{m}-A_{y}^{m}\right)\sin \tau _{B}\\\left(B_{x}^{m}-A_{x}^{m}\right)\cos \tau _{A}+\left(B_{y}^{m}-A_{y}^{m}\right)\sin \tau _{A}\\\end{pmatrix}}.}
3848:
1515:
1903:
20:
85:
3616:
1163:
3644:
1571:
3274:
1510:{\displaystyle {\begin{aligned}P_{x}&=A_{x}^{m}+d_{A}\cos \left(\tau _{A}-{\frac {\pi }{2}}\right)\\&=B_{x}^{m}+d_{B}\cos \left(\tau _{B}-{\frac {\pi }{2}}\right);\\P_{y}&=A_{y}^{m}+d_{A}\sin \left(\tau _{A}-{\frac {\pi }{2}}\right)\\&=B_{y}^{m}+d_{B}\sin \left(\tau _{B}-{\frac {\pi }{2}}\right).\end{aligned}}}
1898:{\displaystyle {\begin{pmatrix}1&0&-\sin \tau _{A}&0\\1&0&0&-\sin \tau _{B}\\0&1&\cos \tau _{A}&0\\0&1&0&\cos \tau _{B}\end{pmatrix}}{\begin{pmatrix}P_{x}\\P_{y}\\d_{A}\\d_{B}\end{pmatrix}}={\begin{pmatrix}A_{x}^{m}\\B_{x}^{m}\\A_{y}^{m}\\B_{y}^{m}\end{pmatrix}}.}
3265:
3660:
Consider the planar movement of a circular wheel rolling without slipping on a linear road; see sketch 3. The wheel rotates around its axis M, which translates in a direction parallel to the road. The point of contact P of the wheel with road does not slip, which means the point P has zero velocity
3879:
If two planar rigid bodies are in contact, and each body has its own distinct center of rotation, then the relative center of rotation between the bodies has to lie somewhere on the line connecting the two centers. As a result, since pure rolling can only exist when the center of rotation is at the
3838:
The further a point in the wheel is from the instant center P, the proportionally larger its speed. Therefore, the point at the top of the wheel moves in the same direction as the center M of the wheel, but twice as fast, since it is twice the distance away from P. All points that are a distance
4053:
Since this instant center of rotation P is the center for all points on the body BAC for any random point, say point C, the speed and direction of movement may be determined: connect P to C. The direction of movement of point C is perpendicular to this connection. The speed is proportional to the
3668:
The velocity vector of a point A in the wheel is perpendicular to the segment AP and is proportional to the length of this segment. In particular, the velocities of points in the wheel are determined by the angular velocity of the wheel in rotation around P. The velocity vectors of a number of
953:
3655:
Instant centre of rotation of a rolling wheel broken down into points. By breaking down the rolling wheel into several points, it can be more easily seen how all points of the wheel rotate around a single point at each instant. This point is the instant centre of rotation, shown in
632:
406:
123:
If the two positions of a body are separated by an instant of time in a planar movement, then the pole of a displacement becomes the instant center. In this case, the segments constructed between the instantaneous positions of the points A and B become the velocity vectors
3611:{\displaystyle P_{x}={\frac {B_{y}^{m}-A_{y}^{m}+A_{x}^{m}\tan \tau _{A}-B_{x}^{m}\tan \tau _{B}}{\tan \tau _{A}-\tan \tau _{B}}},\qquad P_{y}={\frac {B_{y}^{m}-A_{y}^{m}+\tan \tau _{A}\left(A_{x}^{m}-B_{x}^{m}\right)}{\tan \tau _{A}-\tan \tau _{B}}}+B_{y}^{m}}
3884:
design as the pitch point, where there is no relative sliding between the gears. In fact, the gearing ratio between the two rotating parts is found by the ratio of the two distances to the relative center. In the example in Sketch 4 the gearing ratio is
3664:
The set of points of the moving wheel that become instant centers is the circle itself, which defines the moving centrode. The points in the fixed plane that correspond to these instant centers is the line of the road, which defines the fixed centrode.
3839:
equal to the radius of the wheel 'r' from point P move at the same speed as the point M but in different directions. This is shown for a point on the wheel that has the same speed as M but moves in the direction tangent to the circle around P.
119:
to the two segments AA and BB. The intersection P of these two bisectors is the pole of the planar displacement. Notice that A and A lie on a circle around P. This is true for the corresponding positions of every point in the body.
3064:
4007:
For determining the instant center of rotation of the third element of the linkage, the body BAC, the two points A and B are used because its moving characteristics are known, as derived from the information about the links
751:
3634:
In the limit, pure translation becomes planar movement with point velocity vectors that are parallel. In this case, the instant center is said to lie at infinity in the direction perpendicular to the velocity vectors.
47:) of a body undergoing planar movement is a point that has zero velocity at a particular instant of time. At this instant, the velocity vectors of the other points in the body generate a circular field around this
4065:-B rotating around their own instant centers of rotation the centrode for instant center of rotation P may be determined. From this the path of movement for C or any other point on body BAC may be determined.
2987:
2897:
3880:
point of contact (as seen above with the wheel on the road), it is only when the point of contact goes through the line connecting the two rotation centers that pure rolling can be achieved. This is known in
3736:
471:
245:
3626:
If the displacement between two positions is a pure translation, then the perpendicular bisectors of the segments AB and AB form parallel lines. These lines are considered to intersect at a point on the
1168:
107:. For any planar displacement there is a point in the moving body that is in the same place before and after the displacement. The displacement can be viewed as a rotation around this pole.
72:
The generalization of this concept to 3-dimensional space is that of a twist around a screw. The screw has an axis which is a line in 3D space (not necessarily through the origin), the
3042:
1011:
3926:
1072:
183:
2740:
3797:
3833:
2786:
4380:
4073:
In biomechanical research the instant center of rotation is observed for the functioning of the joints in the upper and lower extremities. For example, in analysing the
3768:
1154:
1126:
1099:
743:
716:
689:
662:
463:
436:
237:
210:
4124:
in front view, the perpendiculars to the velocity lie along the links joining the grounded link to the coupler link. This construction is used to establish the
3260:{\displaystyle {\begin{cases}P_{y}-A_{y}^{m}=\tan \tau _{A}\left(P_{x}-A_{x}^{m}\right)\\P_{y}-B_{y}^{m}=\tan \tau _{B}\left(P_{x}-B_{x}^{m}\right)\end{cases}}}
2806:
1563:
1543:
115:
First, select two points A and B in the moving body and locate the corresponding points in the two positions; see the illustration. Construct the perpendicular
4250:
Moorehead JD, Montgomery SC, Harvey DM (Sep 2003). "Instant center of rotation estimation using the
Reuleaux technique and a Lateral Extrapolation technique".
4096:
Study of the joints of horses: "...velocity vectors determined from the instant centers of rotation indicated that the joint surfaces slide on each other."
4238:
948:{\displaystyle \tan \tau _{A}={\frac {A_{y}^{2}-A_{y}^{1}}{A_{x}^{2}-A_{x}^{1}}},\quad \tan \tau _{B}={\frac {B_{y}^{2}-B_{y}^{1}}{B_{x}^{2}-B_{x}^{1}}}}
4577:
4558:
4539:
4431:
4504:
4446:
4477:
Colahan P, Piotrowski G, Poulos P (Sep 1988). "Kinematic analysis of the instant centers of rotation of the equine metacarpophalangeal joint".
3651:
4285:
Hollman JH, Deusinger RH, Van Dillen LR, Matava MJ (Aug 2003). "Gender differences in surface rolling and gliding kinematics of the knee".
4034:
What applies to point A also applies to point B, therefore this instant center of rotation P is located on a line perpendicular to vector V
4329:
65:
The continuous movement of a plane has an instant center for every value of the time parameter. This generates a curve called the moving
3867:. Since the parts cannot interpenetrate the relative rotation center must also be along the normal direction to the contact and through
2904:
2814:
627:{\displaystyle B_{x}^{m}={\frac {1}{2}}\left(B_{x}^{1}+B_{x}^{2}\right);\quad B_{y}^{m}={\frac {1}{2}}\left(B_{y}^{1}+B_{y}^{2}\right).}
401:{\displaystyle A_{x}^{m}={\frac {1}{2}}\left(A_{x}^{1}+A_{x}^{2}\right);\quad A_{y}^{m}={\frac {1}{2}}\left(A_{y}^{1}+A_{y}^{2}\right),}
3675:
3661:
with respect to the road. Thus, at the instant the point P on the wheel comes in contact with the road it becomes an instant center.
3973:
is the only point not moving in the given plane it may be called the instant center of rotation for this link. Point A, at distance P
4027:
is tangentially located on the circumference of a circle). The only line that fills the requirement is a line colinear with link P
3939:
where a number of instant centers of rotation are illustrated. The rigid body noted by the letters BAC is connected with links P
62:. The instant center is the point in the moving plane around which all other points are rotating at a specific instant of time.
4587:
76:; the screw also has a finite pitch (a fixed translation along its axis corresponding to a rotation about the screw axis).
3631:, thus the pole of this planar displacement is said to "lie at infinity" in the direction of the perpendicular bisectors.
4214:
4330:"Changes in Achilles tendon moment arm from rest to maximum isometric plantarflexion: in vivo observations in man"
1021:
2994:
963:
3888:
1027:
138:
4609:
4171:
4000:
is the instant center of rotation for this link and point B moves in the direction as indicated by vector V
2684:
4624:
4121:
1522:
4554:
4535:
4511:
4427:
3773:
4453:
4367:
3802:
3073:
4181:
2745:
96:
4042:-B. Therefore, the instant center of rotation P of body BAC is the point where the lines through P
1908:
The coordinates of the center of the rotation are the first two components of the solution vector
3958:-B, and body BAC. For each of these three parts an instant center of rotation may be determined.
4031:-A. Somewhere on this line there is a point P, the instant center of rotation for the body BAC.
3744:
69:. The points in the fixed plane corresponding to these instant centers form the fixed centrode.
4156:
3052:
58:
Planar movement of a body is often described using a plane figure moving in a two-dimensional
4146:
104:
92:
The instant center can be considered the limiting case of the pole of a planar displacement.
1131:
4110:
characteristics of a car may be improved by varying the design of a brake pedal mechanism.
1104:
1077:
721:
694:
667:
640:
441:
414:
215:
188:
8:
4614:
4202:
Illustrated
Dictionary of Mechanical Engineering: English, German, French, Dutch, Russian
4354:
4310:
4298:
3669:
points are illustrated in sketch 3 and can be calculated using the following equation:
2791:
1548:
1528:
48:
4263:
132:. The lines perpendicular to these velocity vectors intersect in the instant center.
4619:
4583:
4486:
4409:
4405:
4359:
4345:
4302:
4267:
4314:
4401:
4349:
4341:
4294:
4259:
4141:
4117:
4086:
3936:
3628:
73:
59:
99:
of a body from position 1 to position 2 is defined by the combination of a planar
1128:
to the two midpoints. Assuming clockwise rotation (otherwise switch the sign of
4392:
Poppen NK, Walker PS (Mar 1976). "Normal and abnormal motion of the shoulder".
3842:
4603:
4573:
4100:
3950:
The three moving parts of this mechanism (the base is not moving) are: link P
3881:
4306:
4271:
4218:
4023:. Its instant center of rotation must be perpendicular to this vector (as V
3847:
4490:
4413:
4363:
4166:
4128:
3056:
4544: Variable Mechanical Ratio Brake Pedal Mounts - General Motors, 1976
3851:
Sketch 4: Example relative center of rotation. Two bodies in contact at
745:
measured counter-clockwise relative to the horizontal are determined by
4176:
4161:
4090:
3981:, moves in a circular motion in a direction perpendicular to the link P
2678:
Find equations of the bisectors of two segments AA and BB as follows
4125:
3965:-A: all points on this link, including point A, rotate around point P
3638:
116:
19:
84:
4151:
4082:
66:
52:
2982:{\displaystyle y-B_{y}^{m}=\tan \tau _{B}\left(x-B_{x}^{m}\right)}
2892:{\displaystyle y-A_{y}^{m}=\tan \tau _{A}\left(x-A_{x}^{m}\right)}
4204:(Springer Science & Business Media, 17 Apr. 2013 - 422 pages)
3863:
must have a relative center of rotation somewhere along the line
4284:
3731:{\displaystyle {\vec {v}}={\vec {\omega }}\times {\vec {r}}_{A}}
3643:
100:
4327:
4107:
4078:
3871:. The only possible solution is if the relative center is at
3930:
3843:
Relative center of rotation for two contacting planar bodies
4074:
3253:
4019:
The direction of speed of point A is indicated by vector V
2681:
The equation of a straight line in point- slope form is:
4249:
135:
The algebraic construction of the
Cartesian coordinates
4476:
4328:
Maganaris CN, Baltzopoulos V, Sargeant AJ (Aug 1998).
2042:
1923:
1809:
1738:
1580:
3891:
3805:
3776:
3747:
3678:
3277:
3067:
2997:
2907:
2817:
2794:
2748:
2687:
1917:
1574:
1551:
1531:
1166:
1134:
1107:
1080:
1030:
966:
754:
724:
697:
670:
643:
474:
444:
417:
248:
218:
191:
141:
4113:
Designing the suspension of a bicycle, or of a car.
3920:
3827:
3791:
3762:
3730:
3639:Instant center of a wheel rolling without slipping
3610:
3259:
3036:
2981:
2891:
2800:
2780:
2734:
2662:
1897:
1557:
1537:
1509:
1148:
1120:
1093:
1066:
1005:
947:
737:
710:
683:
656:
626:
457:
430:
400:
231:
204:
177:
111:Construction for the pole of a planar displacement
51:which is identical to what is generated by a pure
185:can be arranged as follows: The midpoint between
4601:
79:
16:Point fixed to a body undergoing planar movement
4572:
4239:Knee joint motion description and measurement
4085:joints. Such knowledge assists in developing
4057:Continuing this approach with the two links P
4505:"PART VI Vessel Navigation and Manoeuvering"
4391:
4215:"Muscle Physiology — Joint Moment Arm"
4068:
4353:
3931:Instant center of rotation and mechanisms
3037:{\displaystyle P\left(P_{x},P_{y}\right)}
1006:{\displaystyle P\left(P_{x},P_{y}\right)}
4579:Vehicle Dynamics: Theory and Application
3921:{\displaystyle \gamma ={\frac {AD}{BD}}}
3846:
3650:
3642:
1067:{\displaystyle \left(P_{x},P_{y}\right)}
178:{\displaystyle \left(P_{x},P_{y}\right)}
83:
18:
2901:The equation of the bisector of BB is
2811:The equation of the bisector of AA is
88:Sketch 2: Pole of a planar displacement
4602:
1521:Rewrite this as a 4 × 4 inhomogeneous
4116:In the case of the coupler link in a
4563: Bicycle rear suspension system
4093:, such as elbow or finger joints.
1525:with 4 unknowns (the two distances
1020:Taking the correct branches of the
13:
4299:10.1097/01.blo.0000072902.36018.fe
2991:These two bisectors intersect at
2735:{\displaystyle y-y_{0}=m(x-x_{0})}
14:
4636:
4447:"Pyrocarbon Finger Joint Implant"
4406:10.2106/00004623-197658020-00006
4346:10.1111/j.1469-7793.1998.977bj.x
3792:{\displaystyle {\vec {\omega }}}
4566:
4547:
4528:
4497:
4470:
4439:
3438:
3269:The solution of this system is
1074:of the rotation have distances
851:
549:
323:
23:Sketch 1: Instantaneous center
4420:
4385:
4374:
4321:
4278:
4243:
4232:
4207:
4195:
3828:{\displaystyle {\vec {r}}_{A}}
3813:
3799:angular velocity of wheel and
3783:
3754:
3716:
3700:
3685:
2775:
2749:
2729:
2710:
465:has the Cartesian coordinates
239:has the Cartesian coordinates
1:
4264:10.1016/S0021-9290(03)00156-8
4188:
4038:, a line colinear with link P
2781:{\displaystyle (x_{0},y_{0})}
80:Pole of a planar displacement
37:instantaneous velocity center
4172:Rotation around a fixed axis
3985:-A, as indicated by vector V
7:
4134:
45:pole of planar displacement
10:
4641:
4122:double wishbone suspension
3992:The same applies to link P
3835:vector from point P to A.
3763:{\displaystyle {\vec {v}}}
1523:system of linear equations
33:instant center of rotation
411:and the midpoint between
4381:Biomechanics of shoulder
4182:Two-dimensional rotation
3961:Considering first link P
3770:is velocity of point A,
3647:Sketch 3: Rolling wheel.
1545:and the two coordinates
4069:Examples of application
3947:-B to a base or frame.
3935:Sketch 1 above shows a
4157:Point reflection group
4103:moving through water.
3922:
3876:
3829:
3793:
3764:
3732:
3657:
3648:
3619:
3612:
3261:
3038:
2983:
2893:
2802:
2782:
2736:
2672:
2664:
1899:
1559:
1539:
1511:
1158:
1150:
1149:{\displaystyle \pi /2}
1122:
1095:
1068:
1007:
960:Find the position of
949:
739:
712:
685:
658:
628:
459:
432:
402:
233:
206:
179:
89:
28:
4436: Elbow prosthesis
4334:Journal of Physiology
4287:Clin Orthop Relat Res
4099:Studies on turning a
4054:distance to point P.
3923:
3855:, one rotating about
3850:
3830:
3794:
3765:
3733:
3654:
3646:
3613:
3262:
3039:
2984:
2894:
2803:
2783:
2737:
2676:
2665:
1900:
1560:
1540:
1519:
1512:
1151:
1123:
1121:{\displaystyle d_{B}}
1096:
1094:{\displaystyle d_{A}}
1069:
1018:
1008:
950:
740:
738:{\displaystyle B^{2}}
713:
711:{\displaystyle B^{1}}
686:
684:{\displaystyle A^{2}}
659:
657:{\displaystyle A^{1}}
629:
460:
458:{\displaystyle B^{2}}
433:
431:{\displaystyle B^{1}}
403:
234:
232:{\displaystyle A^{2}}
207:
205:{\displaystyle A^{1}}
180:
87:
22:
4582:. Berlin: Springer.
4394:J Bone Joint Surg Am
3889:
3859:and the other about
3803:
3774:
3745:
3676:
3275:
3065:
2995:
2905:
2815:
2792:
2746:
2685:
1915:
1572:
1549:
1529:
1164:
1132:
1105:
1078:
1028:
964:
752:
722:
695:
668:
641:
637:The two angles from
472:
442:
415:
246:
216:
189:
139:
41:instantaneous center
4610:Classical mechanics
4131:of the suspension.
3607:
3544:
3526:
3487:
3469:
3378:
3344:
3326:
3308:
3244:
3192:
3155:
3103:
2973:
2928:
2883:
2838:
2627:
2609:
2565:
2547:
2502:
2484:
2440:
2422:
2366:
2316:
2261:
2243:
2187:
2137:
2082:
2064:
1883:
1864:
1845:
1826:
1447:
1370:
1279:
1202:
941:
923:
906:
888:
844:
826:
809:
791:
615:
597:
564:
540:
522:
489:
389:
371:
338:
314:
296:
263:
97:planar displacement
4147:Burmester's theory
3918:
3877:
3825:
3789:
3760:
3728:
3658:
3649:
3608:
3593:
3530:
3512:
3473:
3455:
3364:
3330:
3312:
3294:
3257:
3252:
3230:
3178:
3141:
3089:
3034:
2979:
2959:
2914:
2889:
2869:
2824:
2798:
2778:
2732:
2660:
2651:
2613:
2595:
2551:
2533:
2488:
2470:
2426:
2408:
2352:
2302:
2247:
2229:
2173:
2123:
2068:
2050:
1980:
1895:
1886:
1869:
1850:
1831:
1812:
1795:
1727:
1555:
1535:
1507:
1505:
1433:
1356:
1265:
1188:
1146:
1118:
1091:
1064:
1003:
945:
927:
909:
892:
874:
830:
812:
795:
777:
735:
708:
681:
654:
624:
601:
583:
550:
526:
508:
475:
455:
428:
398:
375:
357:
324:
300:
282:
249:
229:
202:
175:
90:
49:center of rotation
29:
4625:Geometric centers
4589:978-0-387-74243-4
4087:artificial joints
3916:
3816:
3786:
3757:
3719:
3703:
3688:
3588:
3433:
2801:{\displaystyle m}
2788:is the point and
2035:
1558:{\displaystyle P}
1538:{\displaystyle d}
1493:
1416:
1325:
1248:
1024:. Let the center
943:
846:
576:
501:
350:
275:
27:of a moving plane
4632:
4594:
4593:
4570:
4564:
4562:
4561:
4557:
4551:
4545:
4543:
4542:
4538:
4532:
4526:
4525:
4523:
4522:
4516:
4510:. Archived from
4509:
4501:
4495:
4494:
4474:
4468:
4467:
4465:
4464:
4458:
4452:. Archived from
4451:
4443:
4437:
4435:
4434:
4430:
4424:
4418:
4417:
4389:
4383:
4378:
4372:
4371:
4366:. Archived from
4357:
4340:(Pt 3): 977–85.
4325:
4319:
4318:
4282:
4276:
4275:
4247:
4241:
4236:
4230:
4229:
4227:
4226:
4217:. Archived from
4211:
4205:
4199:
4142:Angular velocity
4118:four-bar linkage
3937:four-bar linkage
3927:
3925:
3924:
3919:
3917:
3915:
3907:
3899:
3834:
3832:
3831:
3826:
3824:
3823:
3818:
3817:
3809:
3798:
3796:
3795:
3790:
3788:
3787:
3779:
3769:
3767:
3766:
3761:
3759:
3758:
3750:
3737:
3735:
3734:
3729:
3727:
3726:
3721:
3720:
3712:
3705:
3704:
3696:
3690:
3689:
3681:
3629:line at infinity
3622:Pure translation
3617:
3615:
3614:
3609:
3606:
3601:
3589:
3587:
3586:
3585:
3567:
3566:
3550:
3549:
3545:
3543:
3538:
3525:
3520:
3506:
3505:
3486:
3481:
3468:
3463:
3453:
3448:
3447:
3434:
3432:
3431:
3430:
3412:
3411:
3395:
3394:
3393:
3377:
3372:
3360:
3359:
3343:
3338:
3325:
3320:
3307:
3302:
3292:
3287:
3286:
3266:
3264:
3263:
3258:
3256:
3255:
3249:
3245:
3243:
3238:
3226:
3225:
3211:
3210:
3191:
3186:
3174:
3173:
3160:
3156:
3154:
3149:
3137:
3136:
3122:
3121:
3102:
3097:
3085:
3084:
3044:so a system of
3043:
3041:
3040:
3035:
3033:
3029:
3028:
3027:
3015:
3014:
2988:
2986:
2985:
2980:
2978:
2974:
2972:
2967:
2947:
2946:
2927:
2922:
2898:
2896:
2895:
2890:
2888:
2884:
2882:
2877:
2857:
2856:
2837:
2832:
2807:
2805:
2804:
2799:
2787:
2785:
2784:
2779:
2774:
2773:
2761:
2760:
2741:
2739:
2738:
2733:
2728:
2727:
2703:
2702:
2669:
2667:
2666:
2661:
2656:
2655:
2648:
2647:
2632:
2628:
2626:
2621:
2608:
2603:
2586:
2585:
2570:
2566:
2564:
2559:
2546:
2541:
2523:
2522:
2507:
2503:
2501:
2496:
2483:
2478:
2461:
2460:
2445:
2441:
2439:
2434:
2421:
2416:
2398:
2397:
2382:
2381:
2365:
2360:
2348:
2347:
2332:
2331:
2315:
2310:
2298:
2297:
2282:
2281:
2266:
2262:
2260:
2255:
2242:
2237:
2219:
2218:
2203:
2202:
2186:
2181:
2169:
2168:
2153:
2152:
2136:
2131:
2119:
2118:
2103:
2102:
2087:
2083:
2081:
2076:
2063:
2058:
2036:
2034:
2033:
2029:
2028:
2027:
2015:
2014:
1990:
1985:
1984:
1977:
1976:
1963:
1962:
1949:
1948:
1935:
1934:
1904:
1902:
1901:
1896:
1891:
1890:
1882:
1877:
1863:
1858:
1844:
1839:
1825:
1820:
1800:
1799:
1792:
1791:
1778:
1777:
1764:
1763:
1750:
1749:
1732:
1731:
1724:
1723:
1684:
1683:
1654:
1653:
1611:
1610:
1565:of the center):
1564:
1562:
1561:
1556:
1544:
1542:
1541:
1536:
1516:
1514:
1513:
1508:
1506:
1499:
1495:
1494:
1486:
1481:
1480:
1460:
1459:
1446:
1441:
1426:
1422:
1418:
1417:
1409:
1404:
1403:
1383:
1382:
1369:
1364:
1348:
1347:
1331:
1327:
1326:
1318:
1313:
1312:
1292:
1291:
1278:
1273:
1258:
1254:
1250:
1249:
1241:
1236:
1235:
1215:
1214:
1201:
1196:
1180:
1179:
1155:
1153:
1152:
1147:
1142:
1127:
1125:
1124:
1119:
1117:
1116:
1100:
1098:
1097:
1092:
1090:
1089:
1073:
1071:
1070:
1065:
1063:
1059:
1058:
1057:
1045:
1044:
1012:
1010:
1009:
1004:
1002:
998:
997:
996:
984:
983:
954:
952:
951:
946:
944:
942:
940:
935:
922:
917:
907:
905:
900:
887:
882:
872:
867:
866:
847:
845:
843:
838:
825:
820:
810:
808:
803:
790:
785:
775:
770:
769:
744:
742:
741:
736:
734:
733:
717:
715:
714:
709:
707:
706:
690:
688:
687:
682:
680:
679:
663:
661:
660:
655:
653:
652:
633:
631:
630:
625:
620:
616:
614:
609:
596:
591:
577:
569:
563:
558:
545:
541:
539:
534:
521:
516:
502:
494:
488:
483:
464:
462:
461:
456:
454:
453:
437:
435:
434:
429:
427:
426:
407:
405:
404:
399:
394:
390:
388:
383:
370:
365:
351:
343:
337:
332:
319:
315:
313:
308:
295:
290:
276:
268:
262:
257:
238:
236:
235:
230:
228:
227:
211:
209:
208:
203:
201:
200:
184:
182:
181:
176:
174:
170:
169:
168:
156:
155:
74:axis of rotation
4640:
4639:
4635:
4634:
4633:
4631:
4630:
4629:
4600:
4599:
4598:
4597:
4590:
4571:
4567:
4559:
4553:
4552:
4548:
4540:
4534:
4533:
4529:
4520:
4518:
4514:
4507:
4503:
4502:
4498:
4475:
4471:
4462:
4460:
4456:
4449:
4445:
4444:
4440:
4432:
4426:
4425:
4421:
4390:
4386:
4379:
4375:
4326:
4322:
4293:(413): 208–21.
4283:
4279:
4248:
4244:
4237:
4233:
4224:
4222:
4213:
4212:
4208:
4200:
4196:
4191:
4186:
4137:
4071:
4064:
4060:
4049:
4045:
4041:
4037:
4030:
4026:
4022:
4015:
4011:
4003:
3999:
3995:
3988:
3984:
3980:
3976:
3972:
3968:
3964:
3957:
3953:
3946:
3942:
3933:
3908:
3900:
3898:
3890:
3887:
3886:
3845:
3819:
3808:
3807:
3806:
3804:
3801:
3800:
3778:
3777:
3775:
3772:
3771:
3749:
3748:
3746:
3743:
3742:
3722:
3711:
3710:
3709:
3695:
3694:
3680:
3679:
3677:
3674:
3673:
3641:
3602:
3597:
3581:
3577:
3562:
3558:
3551:
3539:
3534:
3521:
3516:
3511:
3507:
3501:
3497:
3482:
3477:
3464:
3459:
3454:
3452:
3443:
3439:
3426:
3422:
3407:
3403:
3396:
3389:
3385:
3373:
3368:
3355:
3351:
3339:
3334:
3321:
3316:
3303:
3298:
3293:
3291:
3282:
3278:
3276:
3273:
3272:
3251:
3250:
3239:
3234:
3221:
3217:
3216:
3212:
3206:
3202:
3187:
3182:
3169:
3165:
3162:
3161:
3150:
3145:
3132:
3128:
3127:
3123:
3117:
3113:
3098:
3093:
3080:
3076:
3069:
3068:
3066:
3063:
3062:
3059:can be written
3048:equations with
3023:
3019:
3010:
3006:
3005:
3001:
2996:
2993:
2992:
2968:
2963:
2952:
2948:
2942:
2938:
2923:
2918:
2906:
2903:
2902:
2878:
2873:
2862:
2858:
2852:
2848:
2833:
2828:
2816:
2813:
2812:
2793:
2790:
2789:
2769:
2765:
2756:
2752:
2747:
2744:
2743:
2723:
2719:
2698:
2694:
2686:
2683:
2682:
2675:
2650:
2649:
2643:
2639:
2622:
2617:
2604:
2599:
2594:
2590:
2581:
2577:
2560:
2555:
2542:
2537:
2532:
2528:
2525:
2524:
2518:
2514:
2497:
2492:
2479:
2474:
2469:
2465:
2456:
2452:
2435:
2430:
2417:
2412:
2407:
2403:
2400:
2399:
2393:
2389:
2377:
2373:
2361:
2356:
2343:
2339:
2327:
2323:
2311:
2306:
2293:
2289:
2277:
2273:
2256:
2251:
2238:
2233:
2228:
2224:
2221:
2220:
2214:
2210:
2198:
2194:
2182:
2177:
2164:
2160:
2148:
2144:
2132:
2127:
2114:
2110:
2098:
2094:
2077:
2072:
2059:
2054:
2049:
2045:
2038:
2037:
2023:
2019:
2010:
2006:
2005:
2001:
1994:
1989:
1979:
1978:
1972:
1968:
1965:
1964:
1958:
1954:
1951:
1950:
1944:
1940:
1937:
1936:
1930:
1926:
1919:
1918:
1916:
1913:
1912:
1885:
1884:
1878:
1873:
1866:
1865:
1859:
1854:
1847:
1846:
1840:
1835:
1828:
1827:
1821:
1816:
1805:
1804:
1794:
1793:
1787:
1783:
1780:
1779:
1773:
1769:
1766:
1765:
1759:
1755:
1752:
1751:
1745:
1741:
1734:
1733:
1726:
1725:
1719:
1715:
1707:
1702:
1697:
1691:
1690:
1685:
1679:
1675:
1667:
1662:
1656:
1655:
1649:
1645:
1634:
1629:
1624:
1618:
1617:
1612:
1606:
1602:
1591:
1586:
1576:
1575:
1573:
1570:
1569:
1550:
1547:
1546:
1530:
1527:
1526:
1504:
1503:
1485:
1476:
1472:
1471:
1467:
1455:
1451:
1442:
1437:
1424:
1423:
1408:
1399:
1395:
1394:
1390:
1378:
1374:
1365:
1360:
1349:
1343:
1339:
1336:
1335:
1317:
1308:
1304:
1303:
1299:
1287:
1283:
1274:
1269:
1256:
1255:
1240:
1231:
1227:
1226:
1222:
1210:
1206:
1197:
1192:
1181:
1175:
1171:
1167:
1165:
1162:
1161:
1138:
1133:
1130:
1129:
1112:
1108:
1106:
1103:
1102:
1085:
1081:
1079:
1076:
1075:
1053:
1049:
1040:
1036:
1035:
1031:
1029:
1026:
1025:
1017:
992:
988:
979:
975:
974:
970:
965:
962:
961:
958:
936:
931:
918:
913:
908:
901:
896:
883:
878:
873:
871:
862:
858:
839:
834:
821:
816:
811:
804:
799:
786:
781:
776:
774:
765:
761:
753:
750:
749:
729:
725:
723:
720:
719:
702:
698:
696:
693:
692:
675:
671:
669:
666:
665:
648:
644:
642:
639:
638:
610:
605:
592:
587:
582:
578:
568:
559:
554:
535:
530:
517:
512:
507:
503:
493:
484:
479:
473:
470:
469:
449:
445:
443:
440:
439:
422:
418:
416:
413:
412:
384:
379:
366:
361:
356:
352:
342:
333:
328:
309:
304:
291:
286:
281:
277:
267:
258:
253:
247:
244:
243:
223:
219:
217:
214:
213:
196:
192:
190:
187:
186:
164:
160:
151:
147:
146:
142:
140:
137:
136:
131:
127:
82:
35:(also known as
17:
12:
11:
5:
4638:
4628:
4627:
4622:
4617:
4612:
4596:
4595:
4588:
4565:
4546:
4527:
4496:
4469:
4438:
4419:
4400:(2): 195–201.
4384:
4373:
4370:on 2012-09-08.
4320:
4277:
4242:
4231:
4206:
4193:
4192:
4190:
4187:
4185:
4184:
4179:
4174:
4169:
4164:
4159:
4154:
4149:
4144:
4138:
4136:
4133:
4070:
4067:
4062:
4058:
4047:
4043:
4039:
4035:
4028:
4024:
4020:
4013:
4009:
4001:
3997:
3993:
3986:
3982:
3978:
3974:
3970:
3966:
3962:
3955:
3951:
3944:
3940:
3932:
3929:
3914:
3911:
3906:
3903:
3897:
3894:
3844:
3841:
3822:
3815:
3812:
3785:
3782:
3756:
3753:
3739:
3738:
3725:
3718:
3715:
3708:
3702:
3699:
3693:
3687:
3684:
3640:
3637:
3605:
3600:
3596:
3592:
3584:
3580:
3576:
3573:
3570:
3565:
3561:
3557:
3554:
3548:
3542:
3537:
3533:
3529:
3524:
3519:
3515:
3510:
3504:
3500:
3496:
3493:
3490:
3485:
3480:
3476:
3472:
3467:
3462:
3458:
3451:
3446:
3442:
3437:
3429:
3425:
3421:
3418:
3415:
3410:
3406:
3402:
3399:
3392:
3388:
3384:
3381:
3376:
3371:
3367:
3363:
3358:
3354:
3350:
3347:
3342:
3337:
3333:
3329:
3324:
3319:
3315:
3311:
3306:
3301:
3297:
3290:
3285:
3281:
3254:
3248:
3242:
3237:
3233:
3229:
3224:
3220:
3215:
3209:
3205:
3201:
3198:
3195:
3190:
3185:
3181:
3177:
3172:
3168:
3164:
3163:
3159:
3153:
3148:
3144:
3140:
3135:
3131:
3126:
3120:
3116:
3112:
3109:
3106:
3101:
3096:
3092:
3088:
3083:
3079:
3075:
3074:
3072:
3032:
3026:
3022:
3018:
3013:
3009:
3004:
3000:
2977:
2971:
2966:
2962:
2958:
2955:
2951:
2945:
2941:
2937:
2934:
2931:
2926:
2921:
2917:
2913:
2910:
2887:
2881:
2876:
2872:
2868:
2865:
2861:
2855:
2851:
2847:
2844:
2841:
2836:
2831:
2827:
2823:
2820:
2808:is the slope.
2797:
2777:
2772:
2768:
2764:
2759:
2755:
2751:
2731:
2726:
2722:
2718:
2715:
2712:
2709:
2706:
2701:
2697:
2693:
2690:
2673:
2671:
2670:
2659:
2654:
2646:
2642:
2638:
2635:
2631:
2625:
2620:
2616:
2612:
2607:
2602:
2598:
2593:
2589:
2584:
2580:
2576:
2573:
2569:
2563:
2558:
2554:
2550:
2545:
2540:
2536:
2531:
2527:
2526:
2521:
2517:
2513:
2510:
2506:
2500:
2495:
2491:
2487:
2482:
2477:
2473:
2468:
2464:
2459:
2455:
2451:
2448:
2444:
2438:
2433:
2429:
2425:
2420:
2415:
2411:
2406:
2402:
2401:
2396:
2392:
2388:
2385:
2380:
2376:
2372:
2369:
2364:
2359:
2355:
2351:
2346:
2342:
2338:
2335:
2330:
2326:
2322:
2319:
2314:
2309:
2305:
2301:
2296:
2292:
2288:
2285:
2280:
2276:
2272:
2269:
2265:
2259:
2254:
2250:
2246:
2241:
2236:
2232:
2227:
2223:
2222:
2217:
2213:
2209:
2206:
2201:
2197:
2193:
2190:
2185:
2180:
2176:
2172:
2167:
2163:
2159:
2156:
2151:
2147:
2143:
2140:
2135:
2130:
2126:
2122:
2117:
2113:
2109:
2106:
2101:
2097:
2093:
2090:
2086:
2080:
2075:
2071:
2067:
2062:
2057:
2053:
2048:
2044:
2043:
2041:
2032:
2026:
2022:
2018:
2013:
2009:
2004:
2000:
1997:
1993:
1988:
1983:
1975:
1971:
1967:
1966:
1961:
1957:
1953:
1952:
1947:
1943:
1939:
1938:
1933:
1929:
1925:
1924:
1922:
1906:
1905:
1894:
1889:
1881:
1876:
1872:
1868:
1867:
1862:
1857:
1853:
1849:
1848:
1843:
1838:
1834:
1830:
1829:
1824:
1819:
1815:
1811:
1810:
1808:
1803:
1798:
1790:
1786:
1782:
1781:
1776:
1772:
1768:
1767:
1762:
1758:
1754:
1753:
1748:
1744:
1740:
1739:
1737:
1730:
1722:
1718:
1714:
1711:
1708:
1706:
1703:
1701:
1698:
1696:
1693:
1692:
1689:
1686:
1682:
1678:
1674:
1671:
1668:
1666:
1663:
1661:
1658:
1657:
1652:
1648:
1644:
1641:
1638:
1635:
1633:
1630:
1628:
1625:
1623:
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4591:
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4575:
4574:Reza N. Jazar
4569:
4556:
4550:
4537:
4531:
4517:on 2009-12-15
4513:
4506:
4500:
4492:
4488:
4485:(9): 1560–5.
4484:
4480:
4473:
4459:on 2011-07-21
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4258:(9): 1301–7.
4257:
4253:
4246:
4240:
4235:
4221:on 2021-02-27
4220:
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3990:
3959:
3948:
3938:
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3895:
3892:
3883:
3882:involute gear
3874:
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2204:
2199:
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2188:
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2178:
2174:
2170:
2165:
2161:
2157:
2154:
2149:
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2141:
2138:
2133:
2128:
2124:
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2115:
2111:
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2104:
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1468:
1464:
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1419:
1413:
1410:
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1400:
1396:
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1371:
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1189:
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1113:
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1023:
1014:
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993:
989:
985:
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937:
932:
928:
924:
919:
914:
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902:
897:
893:
889:
884:
879:
875:
868:
863:
859:
855:
852:
848:
840:
835:
831:
827:
822:
817:
813:
805:
800:
796:
792:
787:
782:
778:
771:
766:
762:
758:
755:
748:
747:
746:
730:
726:
703:
699:
676:
672:
649:
645:
621:
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611:
606:
602:
598:
593:
588:
584:
579:
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560:
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546:
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536:
531:
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446:
423:
419:
395:
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367:
362:
358:
353:
347:
344:
339:
334:
329:
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316:
310:
305:
301:
297:
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272:
269:
264:
259:
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250:
242:
241:
240:
224:
220:
197:
193:
171:
165:
161:
157:
152:
148:
143:
133:
121:
118:
113:
112:
108:
106:
102:
98:
93:
86:
77:
75:
70:
68:
63:
61:
56:
54:
50:
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42:
38:
34:
26:
21:
4578:
4568:
4549:
4530:
4519:. Retrieved
4512:the original
4499:
4482:
4479:Am J Vet Res
4478:
4472:
4461:. Retrieved
4454:the original
4441:
4422:
4397:
4393:
4387:
4376:
4368:the original
4337:
4333:
4323:
4290:
4286:
4280:
4255:
4251:
4245:
4234:
4223:. Retrieved
4219:the original
4209:
4201:
4197:
4120:, such as a
4115:
4112:
4105:
4098:
4095:
4072:
4056:
4052:
4033:
4018:
4006:
3991:
3960:
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3872:
3868:
3864:
3860:
3856:
3852:
3837:
3740:
3667:
3663:
3659:
3633:
3625:
3621:
3620:
3271:
3268:
3061:
3057:coefficients
3049:
3045:
2990:
2900:
2810:
2680:
2677:
1907:
1520:
1019:
959:
957:
636:
410:
134:
122:
114:
110:
109:
94:
91:
71:
64:
57:
44:
40:
36:
32:
30:
24:
4167:Roll center
4129:roll center
3996:-B: point P
105:translation
103:and planar
4615:Kinematics
4604:Categories
4555:US 7100930
4536:GB 1443270
4521:2008-08-22
4463:2008-08-22
4428:US 5030237
4225:2008-08-22
4189:References
4177:Screw axis
4162:Rigid body
4091:prosthesis
4050:-B cross.
3954:-A, link P
2674:Method 2:
1016:Method 1:
4252:J Biomech
4126:kinematic
3977:-A from P
3969:. Since P
3893:γ
3814:→
3784:→
3781:ω
3755:→
3717:→
3707:×
3701:→
3698:ω
3686:→
3579:τ
3575:
3569:−
3560:τ
3556:
3528:−
3499:τ
3495:
3471:−
3424:τ
3420:
3414:−
3405:τ
3401:
3387:τ
3383:
3362:−
3353:τ
3349:
3310:−
3228:−
3204:τ
3200:
3176:−
3139:−
3115:τ
3111:
3087:−
2957:−
2940:τ
2936:
2912:−
2867:−
2850:τ
2846:
2822:−
2717:−
2692:−
2641:τ
2637:
2611:−
2579:τ
2575:
2549:−
2516:τ
2512:
2486:−
2454:τ
2450:
2424:−
2391:τ
2387:
2375:τ
2371:
2350:−
2341:τ
2337:
2325:τ
2321:
2291:τ
2287:
2275:τ
2271:
2245:−
2212:τ
2208:
2196:τ
2192:
2171:−
2162:τ
2158:
2146:τ
2142:
2112:τ
2108:
2096:τ
2092:
2066:−
2021:τ
2017:−
2008:τ
1999:
1717:τ
1713:
1677:τ
1673:
1647:τ
1643:
1637:−
1604:τ
1600:
1594:−
1488:π
1483:−
1474:τ
1465:
1411:π
1406:−
1397:τ
1388:
1320:π
1315:−
1306:τ
1297:
1243:π
1238:−
1229:τ
1220:
1136:π
925:−
890:−
860:τ
856:
828:−
793:−
763:τ
759:
691:and from
117:bisectors
4620:Rotation
4576:(2008).
4315:45191914
4307:12897612
4272:12893038
4152:Centrode
4135:See also
4083:shoulder
4061:-A and P
4046:-A and P
4012:-A and P
3943:-A and P
3053:unknowns
101:rotation
67:centrode
53:rotation
4491:3223666
4414:1254624
4364:9660906
4355:2231068
4108:braking
2742:where
1022:tangent
4586:
4560:
4541:
4489:
4433:
4412:
4362:
4352:
4313:
4305:
4270:
4101:vessel
3741:where
3656:black.
4515:(PDF)
4508:(PDF)
4457:(PDF)
4450:(PDF)
4311:S2CID
4081:, or
4079:ankle
128:and V
60:plane
43:, or
4584:ISBN
4487:PMID
4410:PMID
4360:PMID
4303:PMID
4268:PMID
4106:The
4089:and
4075:knee
4016:-B.
3055:and
1101:and
438:and
212:and
95:The
31:The
4402:doi
4350:PMC
4342:doi
4338:510
4295:doi
4291:413
4260:doi
3572:tan
3553:tan
3492:tan
3417:tan
3398:tan
3380:tan
3346:tan
3197:tan
3108:tan
2933:tan
2843:tan
2634:sin
2572:cos
2509:sin
2447:cos
2384:sin
2368:cos
2334:cos
2318:sin
2284:cos
2268:cos
2205:sin
2189:cos
2155:cos
2139:sin
2105:sin
2089:sin
1996:sin
1710:cos
1670:cos
1640:sin
1597:sin
1462:sin
1385:sin
1294:cos
1217:cos
853:tan
756:tan
718:to
664:to
4606::
4483:49
4481:.
4408:.
4398:58
4396:.
4358:.
4348:.
4336:.
4332:.
4309:.
4301:.
4289:.
4266:.
4256:36
4254:.
4077:,
4004:.
3989:.
3865:AB
1156:):
55:.
39:,
4592:.
4524:.
4493:.
4466:.
4416:.
4404::
4344::
4317:.
4297::
4274:.
4262::
4228:.
4063:2
4059:1
4048:2
4044:1
4040:2
4036:B
4029:1
4025:A
4021:A
4014:2
4010:1
4008:P
4002:B
3998:2
3994:2
3987:A
3983:1
3979:1
3975:1
3971:1
3967:1
3963:1
3956:2
3952:1
3945:2
3941:1
3913:D
3910:B
3905:D
3902:A
3896:=
3875:.
3873:D
3869:C
3861:B
3857:A
3853:C
3821:A
3811:r
3752:v
3724:A
3714:r
3692:=
3683:v
3604:m
3599:y
3595:B
3591:+
3583:B
3564:A
3547:)
3541:m
3536:x
3532:B
3523:m
3518:x
3514:A
3509:(
3503:A
3489:+
3484:m
3479:y
3475:A
3466:m
3461:y
3457:B
3450:=
3445:y
3441:P
3436:,
3428:B
3409:A
3391:B
3375:m
3370:x
3366:B
3357:A
3341:m
3336:x
3332:A
3328:+
3323:m
3318:y
3314:A
3305:m
3300:y
3296:B
3289:=
3284:x
3280:P
3247:)
3241:m
3236:x
3232:B
3223:x
3219:P
3214:(
3208:B
3194:=
3189:m
3184:y
3180:B
3171:y
3167:P
3158:)
3152:m
3147:x
3143:A
3134:x
3130:P
3125:(
3119:A
3105:=
3100:m
3095:y
3091:A
3082:y
3078:P
3071:{
3050:2
3046:2
3031:)
3025:y
3021:P
3017:,
3012:x
3008:P
3003:(
2999:P
2976:)
2970:m
2965:x
2961:B
2954:x
2950:(
2944:B
2930:=
2925:m
2920:y
2916:B
2909:y
2886:)
2880:m
2875:x
2871:A
2864:x
2860:(
2854:A
2840:=
2835:m
2830:y
2826:A
2819:y
2796:m
2776:)
2771:0
2767:y
2763:,
2758:0
2754:x
2750:(
2730:)
2725:0
2721:x
2714:x
2711:(
2708:m
2705:=
2700:0
2696:y
2689:y
2658:.
2653:)
2645:A
2630:)
2624:m
2619:y
2615:A
2606:m
2601:y
2597:B
2592:(
2588:+
2583:A
2568:)
2562:m
2557:x
2553:A
2544:m
2539:x
2535:B
2530:(
2520:B
2505:)
2499:m
2494:y
2490:A
2481:m
2476:y
2472:B
2467:(
2463:+
2458:B
2443:)
2437:m
2432:x
2428:A
2419:m
2414:x
2410:B
2405:(
2395:B
2379:A
2363:m
2358:y
2354:B
2345:B
2329:A
2313:m
2308:y
2304:A
2300:+
2295:B
2279:A
2264:)
2258:m
2253:x
2249:B
2240:m
2235:x
2231:A
2226:(
2216:B
2200:A
2184:m
2179:x
2175:A
2166:B
2150:A
2134:m
2129:x
2125:B
2121:+
2116:B
2100:A
2085:)
2079:m
2074:y
2070:A
2061:m
2056:y
2052:B
2047:(
2040:(
2031:)
2025:B
2012:A
2003:(
1992:1
1987:=
1982:)
1974:B
1970:d
1960:A
1956:d
1946:y
1942:P
1932:x
1928:P
1921:(
1893:.
1888:)
1880:m
1875:y
1871:B
1861:m
1856:y
1852:A
1842:m
1837:x
1833:B
1823:m
1818:x
1814:A
1807:(
1802:=
1797:)
1789:B
1785:d
1775:A
1771:d
1761:y
1757:P
1747:x
1743:P
1736:(
1729:)
1721:B
1705:0
1700:1
1695:0
1688:0
1681:A
1665:1
1660:0
1651:B
1632:0
1627:0
1622:1
1615:0
1608:A
1589:0
1584:1
1578:(
1553:P
1533:d
1501:.
1497:)
1491:2
1478:B
1469:(
1457:B
1453:d
1449:+
1444:m
1439:y
1435:B
1431:=
1420:)
1414:2
1401:A
1392:(
1380:A
1376:d
1372:+
1367:m
1362:y
1358:A
1354:=
1345:y
1341:P
1333:;
1329:)
1323:2
1310:B
1301:(
1289:B
1285:d
1281:+
1276:m
1271:x
1267:B
1263:=
1252:)
1246:2
1233:A
1224:(
1212:A
1208:d
1204:+
1199:m
1194:x
1190:A
1186:=
1177:x
1173:P
1144:2
1140:/
1114:B
1110:d
1087:A
1083:d
1061:)
1055:y
1051:P
1047:,
1042:x
1038:P
1033:(
1000:)
994:y
990:P
986:,
981:x
977:P
972:(
968:P
938:1
933:x
929:B
920:2
915:x
911:B
903:1
898:y
894:B
885:2
880:y
876:B
869:=
864:B
849:,
841:1
836:x
832:A
823:2
818:x
814:A
806:1
801:y
797:A
788:2
783:y
779:A
772:=
767:A
731:2
727:B
704:1
700:B
677:2
673:A
650:1
646:A
622:.
618:)
612:2
607:y
603:B
599:+
594:1
589:y
585:B
580:(
574:2
571:1
566:=
561:m
556:y
552:B
547:;
543:)
537:2
532:x
528:B
524:+
519:1
514:x
510:B
505:(
499:2
496:1
491:=
486:m
481:x
477:B
451:2
447:B
424:1
420:B
396:,
392:)
386:2
381:y
377:A
373:+
368:1
363:y
359:A
354:(
348:2
345:1
340:=
335:m
330:y
326:A
321:;
317:)
311:2
306:x
302:A
298:+
293:1
288:x
284:A
279:(
273:2
270:1
265:=
260:m
255:x
251:A
225:2
221:A
198:1
194:A
172:)
166:y
162:P
158:,
153:x
149:P
144:(
130:B
126:A
124:V
25:P
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