The paper presents three algorithms for the determination of the actual configuration of the general geometry 6-6 fully-parallel mechanism by using two extra rotary sensors in addition to the six ones that are normally implemented in the servosystems of the six actuated legs. The three proposed algorithms provide a one-to-one correspondence between the sensor measurements and the configuration of the mechanism. Comparison of the three algorithms, that are all for real-time computation, is presented and one of them is shown to be a good compromise between precision and computation time.

1.
Baron, L., and Angeles, J., 1994, “The Decoupling of the Direct Kinematics of Parallel Manipulators Using Redundant Sensors,” Proc. IEEE Int. Robotics and Automation Conf., May 8–13, San Diego, California, pp. 974–979.
2.
Baron, L., and Angeles, J., 1995, “A Linear Algebraic Solution of the Direct Kinematics of Parallel Manipulators Using a Camera,” Proc. Ninth World Congress on the Theory of Machine and Mechanisms, Milano, Italy, pp. 1925–1929.
3.
Cheok
K. C.
,
Overholt
J. L.
, and
Beck
R. R.
,
1993
, “
Exact Method for Determining the Kinemartics of a Stewart Platform Using Additional Displacement Sensors
,”
Journal of Robotic Systems
, Vol.
10
, No.
5
, pp.
689
707
.
4.
Husty, M. L., 1994, “An Algorithm for Solving the Direct Kinematics of the Stewart-Gough-Type Platform,” Private Communication. Also in Mechanism and Machine Theory, Vol. 31, No. 4, 1996, pp. 365–380.
5.
Innocenti
C.
, and
Parenti-Castelli
V.
,
1993
a, “
Forward Kinematics of the General 6-6 Fully Parallel Mechanism: An Exhaustive Numerical Approach Via a Mono-Dimensional Search Algorithm
,”
ASME TRANS., JOURNAL OF MECHANICAL DESIGN
, Vol.
115
, pp.
932
937
.
6.
Innocenti
C.
, and
Parenti-Castelli
V.
,
1993
b, “
Closed Form Direct Position Analysis of a 5-5 Parallel Mechanisim
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
115
, pp.
515
521
.
7.
Innocenti
C.
, and
Parenti-Castelli
V.
,
1993
c, “
Echelon Form Solution of Direct Kinematics for the General Fully-Parallel Spherical Wrist
,”
Mech. Mach. Theory
, Vol.
28
, No.
4
, pp.
553
561
.
8.
Jin, Y., 1994, “Exact Solution for the Forward Kinematics of the General Stewart Platform Using Two Additional Displacement Sensors,” 23rd ASME Biennial Mechanisms Conference, Minneapolis, Minnesota, DE-Vol. 72, pp. 491–495.
9.
Merlet, J. P., 1993, “Closed-Form Resolution of the Direct Kinematics of Parallel Manipulators Using Extra Sensors Data,” Proc. IEEE Int. Robotics and Automation Conf., Atlanta, Georgia, pp. 200–204.
10.
Parenti-Castelli, V., 1992, “Recent Techniques for Direct Position Analysis of the Generalized Stewart Platform Mechanism,” Proceedings of the 3rd International Workshop on Advances In Robot Kinematics, 3ARK, Ferrara, Italy, pp. 129–135.
11.
Parenti-Castelli, V., and Di Gregorio, R., 1995a, “Closed-Form Solution of the Direct Kinematics of the 6-3 Type Stewart Platform Using One Extra Sensor,” Proceedings of XII Congresso Nazionale di Meccanica Teorica ed Applicata, Napoli, Italy, pp. 331–336 (also in Meccanica, Vol. 31, 1996, pp. 705–714).
12.
Parenti-Castelli, V., and Di Gregorio, R., 1995b “Determination of the Actual Configuration of the General Stewart Platform Using Only One Additional Displacement Sensor,” Proc. ASME 1995 International Mechanical Engineering Congress and Exposition, San Francisco, CA, paper No. 95-WA/AD-6.
13.
Raghavan
M.
,
1993
, “
The Stewart Platform of General Geometry has 40 Configurations
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
115
, pp.
277
282
.
14.
Raghavan
M.
, and
Roth
B.
,
1995
, “
Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, pp.
71
79
.
15.
Shi, X., and Fenton, R. G., 1991, “Forward Kinematic Solution of a General 6 DOF Stewart Platform Based on Three Point Position Data,” Proc. of the Eighth World Congress on the Theory of Machines and Mechanisms, Prague, Czechoslovakia, pp. 1015–1018.
16.
Stoughton, R., and Aral, T., 1991, “Optimal Sensor Placement for Forward Kinematics Evaluation of a 6-DOF Parallel Link Manipulator,” IEEE/RSJ International Workshop on Intelligent Robots and Systems IROS’91, Osaka, Japan, pp. 785–790.
17.
Tancredi, L., Teillaud, M., and Merlet, J-P., 1995, “Forward Kinematics of a Parallel Manipulator With Additional Rotary Sensors Measuring the Position of Platform Joints,” Computational Kinematics, J-P. Merlet and B. Ravani Eds., Kluwer Academic Publishers, pp. 261–270.
18.
Wampler
C.
,
Morgan
A.
, and
Sommese
A.
,
1990
Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
112
, pp.
59
68
.
19.
Wen
F., A.
and
Liang
C. G.
,
1994
, “
Displacement Analysis of the General Stewart Platform-Type Mechanism
,”
Mechanism and Machine Theory
, Vol.
29
, No.
4
, pp.
547
557
.
20.
Zanganeh
K., E.
, and
Angeles
J.
,
1995
, “
Real-Time Direct Kinematics of General Six-Degree-of-Freedom Parallel Manipulators With Minimum-Sensor Data
,”
Journal of Robotic Systems
, Vol.
12
, No.
12
, pp.
833
844
.
21.
Zhang
C.
, and
Song
S.
,
1994
, “
Forward Position Analysis of Nearly General Stewart Platforms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, pp.
54
60
.
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