Abstract
The demand for redundant hydraulic manipulators that can implement complex heavy-duty tasks in unstructured areas is increasing; however, current manipulator layouts that remarkably differ from human arms make intuitive kinematic operation challenging to achieve. This study proposes a seven-degree-of-freedom (7-DOF) redundant anthropomorphic hydraulically actuated manipulator with a novel roll-pitch-yaw spherical wrist. A hybrid series-parallel mechanism is presented to achieve the spherical wrist design, which consists of two parallel linear hydraulic cylinders to drive the yaw/pitch 2-DOF wrist plate connected serially to the roll structure. Designed as a 1RPRRR-1SPU mechanism (“R”, “P”, “S”, and “U” denote revolute, prismatic, spherical, and universal joints, respectively; the underlined letter indicates the active joint), the 2-DOF parallel structure is partially decoupled to obtain simple forward/inverse kinematic solutions in which a closed-loop subchain “RPRR” is included. The 7-DOF manipulator is then designed, and its third joint axis goes through the spherical center to obtain closed-form inverse kinematic computation. The analytical inverse kinematic solution is drawn by constructing self-motion manifolds. Finally, a physical prototype is developed, and the kinematic analysis is validated via numerical simulation and test results.
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Abbreviations
- DH:
-
Denavit-Hartenberg
- DOF:
-
Degree of freedom
- HRM:
-
Hydraulic robotic manipulator
- RPR:
-
Roll-pitch-roll
- RPY:
-
Roll-pitch-yaw
- SRS:
-
Sphere-rotation-sphere
- a i(i = 1, 2, …, 7):
-
Link length between two adjacent joints
- b :
-
Length of the vector \(\overrightarrow {BE} \)
- d :
-
Length of the vector \(\overrightarrow {OD} \)
- d i(i = 1, 2, …, 7):
-
Link offset of the joint
- f :
-
Length of the vector \(\overrightarrow {OF} \)
- f j(j = 1, 2, …, g):
-
DOF of wrist joints
- g :
-
Number of wrist joints
- G :
-
Intermediate matrix of the joint angles
- J x :
-
Intermediate matrix of the cylinder displacements
- l 0p :
-
Minimum pitch cylinder length
- l 0y :
-
Minimum yaw cylinder length
- l e :
-
Distance from the wrist center to the endpoint of the manipulator
- M :
-
DOF of the equivalent mechanism
- n :
-
Number of links
- O i(i = 1, 2, …, 7):
-
Center point of the ith joint
- P e :
-
Position of the manipulator endpoint
- P i(i = A, B, …, F):
-
Positions of Points A–F
- q i(i = 1, 2, …, 7):
-
Joint angle of the manipulator
- $ij :
-
Motion screw of the ith joint in the jth limb
- $ rij :
-
Reciprocal screw of the ith joint in the jth limb
- i−1i T(i = 1 2, …, 7):
-
Transformation matrices
- x A, y A, z A :
-
Coordinate of Point A along the x-, y-, and z-axis, respectively
- x C, y C, z C :
-
Coordinate of Point C along the x-, y-, and z-axis, respectively
- x e, y e, z e :
-
Coordinate of the manipulator endpoint along the x-, y-, and z-axis, respectively
- x i, y i, z i(i = 1, 2, …, 7):
-
Coordinate of the center point of the ith joint along the x-, y-, and z-axis, respectively
- x p :
-
Pitch cylinder displacement
- x y :
-
Yaw cylinder displacement
- z 4low, z 4upp :
-
Lower and upper bounds of the z-coordinate of the elbow joint R4, respectively
- α i(i = 1, 2, …, 7):
-
Link wrist angle between two adjacent joints
- θ :
-
Pitch angle of the spherical wrist
- λ :
-
Number of common constraint
- ν :
-
Number of redundancy constraint
- ϕ :
-
Roll angle of the spherical wrist
- ψ :
-
Yaw angle of the spherical wrist
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 91748210 and 51922093), in part by the Natural Science Foundation of Chongqing, China (Grant No. cstc2020jcyj-msxmX0780), and in part by the Fundamental Research Funds for the Central Universities, China (Grant No. 2021CDJKYJH019).
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Cheng, M., Han, Z., Ding, R. et al. Development of a redundant anthropomorphic hydraulically actuated manipulator with a roll-pitch-yaw spherical wrist. Front. Mech. Eng. 16, 698–710 (2021). https://doi.org/10.1007/s11465-021-0646-2
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DOI: https://doi.org/10.1007/s11465-021-0646-2