A CAD variation geometry approach is proposed for accurately solving the Euler angles, Euler angular velocity/acceleration, and the active forces due to a concentrated torque of limited-DOF parallel manipulators (PMs). First, a simulation mechanism of PM with Euler angles, a simulation mechanism of PM with Euler angular velocity/acceleration, and a simulation mechanism of PM with Euler angular torques are created and combined into one simulation mechanism. Second, when modifying the driving dimension of the active legs, the simulation mechanism of PM is varied correspondingly, and the Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved automatically and visualized dynamically. Third, a 3DOF PM and a 5DOF PM are illustrated, and their Euler angles, Euler angular velocity/acceleration, and active forces due to the concentrated torque are solved accurately by CAD variation geometry and are verified by the analytic solutions.
1.
Huang
, Z.
, Kong
, L. -F.
, and Fang
, Y. -F.
, 1997, Theory on Parallel Robotics and Control
, Machinery Industry
, Beijing, China
.2.
Yang
, T. -L.
, 2003, Topology Structure Design of Robot Mechanisms
, China Machine
, Beijing, China
.3.
Tsai
, L. -W.
, and Tahmasebi
, F.
, 1993, “Synthesis and Analysis of a New Class of Six-Degree of Freedom Parallel Minimanipulators
,” J. Rob. Syst.
0741-2223, 10
(5
), pp. 561
–580
.4.
Huang
, Z.
, and Li
, Q. -C.
, 2002, “Type Synthesis Principle of Minor-Mobility Parallel Manipulators
,” Sci. China, Ser. E: Technol. Sci.
1006-9321, 45
(3
), pp. 241
–248
.5.
Dai
, J. -S.
, Huang
, Z.
, and Lipkin
, H.
, 2006, “Mobility of Over Constrained Parallel Mechanisms
,” ASME J. Mech. Des.
0161-8458, 128
(1
), pp. 220
–229
.6.
Gosselin
, C. M.
, Sefrioui
, J.
, and Richard
, M. J.
, 1994, “On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture
,” ASME J. Mech. Des.
0161-8458, 116
(2
), pp. 587
–593
.7.
Stock
, M.
, and Karol
, M.
, 2003, “Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot
,” ASME J. Mech. Des.
0161-8458, 125
(2
), pp. 292
–301
.8.
Lu
, Y.
, and Hu
, B.
, 2008, “Unification and Simplification of Velocity/Acceleration of Limited-DOF Parallel Manipulators With Linear Active Legs
,” Mech. Mach. Theory
0094-114X, 43
(9
), pp. 1112
–1128
.9.
Joshi
, S. A.
, and Tsai
, L. -W.
, 2002, “Jacobian Analysis of Limited-DOF Parallel Manipulators
,” ASME J. Mech. Des.
0161-8458, 124
(2
), pp. 254
–258
.10.
Huang
, Z.
, and Wang
, J.
, 2001, “Kinematics of 3-DOF Pyramid Manipulator by Principal Screws
,” Chin. J. Mech. Eng.
0577-6686, 14
(2
), pp. 116
–120
.11.
Rico
, J. -M.
, Gallardo
, J.
, and Duffy
, J.
, 1999, “Screw Theory and Higher Order Kinematic Analysis of Open Serial and Closed Chains
,” Mech. Mach. Theory
0094-114X, 34
(4
), pp. 559
–586
.12.
Gallardo-Alvarado
, J.
, 2005, “Kinematics of a Hybrid Manipulator by Means of Screw Theory
,” Multibody Syst. Dyn.
1384-5640, 14
(3–4
), pp. 345
–366
.13.
Tsai
, L. -W.
, and Joshi
, S.
, 2000, “Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator
,” ASME J. Mech. Des.
0161-8458, 122
(4
), pp. 439
–446
.14.
Gallardo-Alvarado
, J.
, Rico-Martínez
, J. M.
, and Alici
, G.
, 2006, “Kinematics and Singularity Analyses of a 4-DOF Parallel Manipulator Using Screw Theory
,” Mech. Mach. Theory
0094-114X, 41
(9
), pp. 1048
–1061
.15.
Lu
, Y.
, Hu
, B.
, and Xu
, J. -Y.
, 2008, “Kinematics Analysis and Solution of Active/Passive Forces of a 4SPS+SPR Parallel Machine Tool
,” Int. J. Adv. Manuf. Technol.
, 36
(1–2
), pp. 178
–187
. 0268-376816.
Kim
, S. G.
, and Ryu
, J.
, 2003, “New Dimensionally Homogeneous Jacobian Matrix Formulation by Three End-Effector Points for Optimal Design of Parallel Manipulators
,” IEEE Trans. Rob. Autom.
1042-296X, 19
(4
), pp. 731
–737
.17.
Merlet
, J. P.
, 2006, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,” ASME J. Mech. Des.
0161-8458, 128
(1
), pp. 199
–206
.18.
Altuzarra
, O.
, Salgado
, O.
, Petuya
, V.
, and Hernandez
, A.
, 2006, “Point-Based Jacobian Formulation for Computational Kinematics of Manipulators
,” Mech. Mach. Theory
0094-114X, 41
(12
), pp. 1407
–1423
.19.
Canfield
, S. L.
, Soper
, R. R.
, and Reinholtz
, C. F.
, 1999, “Velocity Analysis of Parallel Manipulators by Truss Transformations
,” Mech. Mach. Theory
0094-114X, 34
(3
), pp. 345
–357
.20.
Zhou
, K.
, Zhao
, J. -S.
, Tan
, Z. -Y.
, and Mao
, D. -Z.
, 2005, “The Kinematics Study of a Class of Spatial Parallel Mechanism With Fewer Degrees of Freedom
,” Int. J. Adv. Manuf. Technol.
, 25
(9–10
), pp. 972
–978
. 0268-376821.
Bonev
, I. A.
, and Jeha
, R.
, 2001, “Geometrical Method for Computing the Constant-Orientation Workspace of 6-PRRS Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 36
(1
), pp. 1
–13
.22.
Bonev
, I. A.
, and Jeha
, R.
, 2001, “A New Approach to Orientation Workspace Analysis of 6-DOF Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 36
(1
), pp. 1
–13
.23.
Lu
, Y.
, 2007, “Simulation Of Machining 3D Free-Form Surface in Normal Direction Using 6-SSP and 4SPS+UPU Parallel Machine Tools
,” Int. J. Adv. Manuf. Technol.
, 33
(11–12
), pp. 1180
–1188
. 0268-376824.
Lu
, Y.
, 2004, “Using CAD Functionalities for the Kinematics Analysis of Spatial Parallel Manipulators With 3-, 4-, 5-, 6-Linearly Driven Limbs
,” Mech. Mach. Theory
0094-114X, 39
(1
), pp. 41
–60
.25.
Lu
, Y.
, 2006, “Using CAD Variation Geometry for Solving Velocity and Acceleration of Parallel Manipulators With 3–5 Linear Driving Limbs
,” ASME J. Mech. Des.
0161-8458, 128
(4
), pp. 738
–746
.26.
Lu
, Y.
, 2007, “Using Virtual Work Theory and CAD Functionalities for Solving Driving Force and Driven Force of Spatial Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 42
(7
), pp. 839
–858
.27.
Lu
, Y.
, and Hu
, B.
, 2006, “Solving Driving Forces of 2(3-SPR) Serial-Parallel Manipulator by CAD Variation Geometry Approach
,” ASME J. Mech. Des.
0161-8458, 128
(6
), pp. 1349
–1351
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