Type Synthesis of Single-Loop Overconstrained 6R Spatial Mechanisms for Circular Translation

To discover single-degree-of-freedom (DOF) single-loop overconstrained mechanisms is still an open problem. This paper deals with the type synthesis of single DOF single-loop overconstrained 6RMCTs (6R spatial mechanisms for circular translation). These mechanisms provide alternatives to planar parallelograms and are also associated with self-motion of several translational parallel mechanisms. 6RMCTs are to be obtained using a construction approach in combination with the approaches to the type synthesis of parallel mechanisms. By imposing certain conditions on the hybrid overconstrained 6R (plano-spherical, plano-Bennett, double-spherical, and spherico-Bennett) mechanisms, Bricard plane symmetric mechanism, and Bricard line symmetric mechanism, six special cases of 6RMCTs are obtained. By combining planar parallelograms with these special mechanisms, the general cases of 6RMCTs are then constructed. Finally, 4R2H, 2R4H, and 6H mechanisms for circular translation are obtained from the above 6RMCTs by replacing one or more pairs of R (revolute) joints with parallel axes each with a pair of H (helical) joints with parallel axes and the same pitch. This work contributes to the research on overconstrained six-bar mechanisms and further reveals that the research areas of parallel mechanisms and single-loop overconstrained mechanisms are closely related.

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A Double-Faced 6R Single-Loop Overconstrained Spatial Mechanism

Journal of Mechanisms and Robotics ◽

10.1115/1.4039224 ◽

2018 ◽

Vol 10 (3) ◽

Cited By ~ 1

Author(s):

Xianwen Kong ◽

Xiuyun He ◽

Duanling Li

Keyword(s):

Kinematic Analysis ◽

Isosceles Triangle ◽

The Other ◽

Dual Quaternion ◽

Single Loop ◽

Plane Symmetric ◽

Spatial Mechanism ◽

Revolute Joints ◽

Full Turn ◽

Overconstrained Mechanisms

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle are also presented in this paper. These formulas will be useful for the design and analysis of multiloop overconstrained mechanisms involving plane symmetric spatial RRR triads.

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Type synthesis of spatial mechanisms for forging manipulators

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406211433246 ◽

2012 ◽

Vol 226 (9) ◽

pp. 2320-2330 ◽

Cited By ~ 10

Author(s):

Yundou Xu ◽

Jiantao Yao ◽

Yongsheng Zhao

Keyword(s):

Degrees Of Freedom ◽

Screw Theory ◽

Parallel Mechanisms ◽

Type Synthesis ◽

Heavy Duty ◽

Systematic Method ◽

Type Selection ◽

Spatial Mechanisms ◽

Selection For ◽

Overconstrained Mechanisms

In this study, a systematic method is proposed to synthesize the parallel and hybrid serial–parallel mechanisms for the forging manipulators based on the screw theory. First, several typical configurations of five-degrees-of-freedom parallel mechanism for the forging manipulators are synthesized, and they are all non-overconstrained mechanisms. Then, two kinds of hybrid serial–parallel mechanisms for the forging manipulators with the advantages of motion decoupling are constructed, which are also not overconstrained. The configurations obtained in this study would provide more type selection for the heavy-duty forging manipulators in engineering.

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Type synthesis of 2R2T parallel mechanisms based on motion equivalent chain method

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214527271 ◽

2014 ◽

Vol 228 (17) ◽

pp. 3209-3217 ◽

Cited By ~ 8

Author(s):

Wei Ye ◽

Yuefa Fang ◽

Sheng Guo ◽

Haibo Qu

Keyword(s):

Parallel Mechanism ◽

Screw Theory ◽

Parallel Mechanisms ◽

Motion Pattern ◽

Type Synthesis ◽

Constraint Force ◽

Single Loop ◽

Loop Chain ◽

Serial Chains

In this paper, the motion equivalent chain method is proposed and then applied to the type synthesis of a class of 2R2T parallel mechanism. The equivalent serial chains are synthesized for a specific 2R2T motion pattern based on screw theory. Feasible limb structures that provide a constraint couple and a constraint force are enumerated according to the reciprocity of the twist and wrench systems. Several motion equivalent single loop chains are constructed with the equivalent serial chains. Using motion equivalent single loop chains to replace the equivalent serial chains, a class of 2R2T parallel mechanisms is obtained based on the foundation of motion equivalent single loop chain structures.

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Type synthesis and kinematics analysis of a family of three translational and one rotational pick-and-place parallel mechanisms with high rotational capability

Advances in Mechanical Engineering ◽

10.1177/1687814019853076 ◽

2019 ◽

Vol 11 (6) ◽

pp. 168781401985307

Author(s):

Xing Zhang ◽

Dejun Mu ◽

Yuze Liu ◽

Jie Bi ◽

Hongrui Wang

Keyword(s):

Parallel Mechanism ◽

Jacobian Matrix ◽

Hessian Matrix ◽

Parallel Mechanisms ◽

Kinematics Analysis ◽

Type Synthesis ◽

Lie Group Theory ◽

Revolute Joints ◽

Pick And Place ◽

Pick And Place Operation

This article proposes a family of spatial three translational and one rotational parallel mechanisms (PMs) for pick-and-place operation. Their features are one independent rotation of the mechanism with four identical limbs, which are provided by the four revolute joints on the moving platform. The rotational capability of the PMs has a range of at least 180°. This article focuses on the synthesis of the PMs and kinematics analysis of the 4- P(2-SS)R parallel mechanism. First, based on the Lie group theory, three parallelograms are used in designing the PMs. The limbs are listed and two types of three translational and one rotational PMs are synthesized. Then, a typical 4- P(2-SS)R PM is selected, the 6 × 6 Jacobian matrix and the 6 × 6 × 6 Hessian matrix of the mechanism are derived for solving the displacement, velocity, and acceleration of the mechanism. Finally, singularity configurations are disclosed from the 6 × 6 Jacobian matrix, and the workspace of the mechanism is provided to illustrate the high rotational capability.

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Type Synthesis of 2-DOF 3-4R Parallel Mechanisms With Both Spatial Parallelogram Translational Mode and Equal-Diameter Spherical Rotation Mode

Volume 5B: 38th Mechanisms and Robotics Conference ◽

10.1115/detc2014-34883 ◽

2014 ◽

Cited By ~ 1

Author(s):

Xianwen Kong ◽

Jingjun Yu

Keyword(s):

Parallel Manipulators ◽

Parallel Mechanisms ◽

Type Synthesis ◽

Rotation Mode ◽

Operation Modes ◽

Translational Mode ◽

The Common ◽

Multiple Operation ◽

Overconstrained Mechanisms

Parallel manipulators (PMs) with multiple operation modes are novel reconfigurable PMs which use less number of actuators and can be reconfigured without disassembly. This paper deals with the type synthesis of 2-DOF PMs with both spatial parallelogram translational mode and equal-diameter spherical rotation mode. At first, a 2-DOF 3-4R overconstrained PM is proposed based on a 5-DOF US equivalent PM proposed in the literature. From this 2-DOF PM, we further obtain a 3-4R PM for equal-diameter spherical rotation and a 3-4R PM for spatial parallelogram translation. By finding the common conditions for the 2-DOF 3-4R PM for spatial parallelogram translation and 2-DOF 3-4R PM for equal-diameter spherical rotation, the types of 2-DOF 3-4R PMs with both spatial parallelogram translational mode and equal-diameter spherical rotation mode are then obtained. This work enriches the types of PMs with multiple operation modes and overconstrained mechanisms.

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On the Mobility of Single Loop N-Bar Linkage With One Prismatic Joint

Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2005-84910 ◽

2005 ◽

Cited By ~ 3

Author(s):

W. Z. Guo ◽

R. Du ◽

J. X. Wang

Keyword(s):

Change Point ◽

Open Loop ◽

Class Iii ◽

Revolute Joint ◽

Single Loop ◽

Prismatic Joint ◽

Revolute Joints ◽

Offset Distance ◽

Special Cases ◽

Prismatic Joints

Single loop N-bar linkages that contain one prismatic joint are common in engineering. This paper presents a systematical study on the mobility of this type of mechanism. It is found that this type of mechanisms can be divided into three categories: Class I, Class II and Class III. For each category, the slide reachable range is cut into different regions: Grashofian region, non-Grashofian region and change-point region. At each region, the rotation range of the revolute joint or rotatability of the linkage is able to determine based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. For active prismatic joint, the input revolute joint(s) is/are dependent in non-Grashofian region but independent in other regions. For passive prismatic joint, the revolvability of input revolute joints is dependent on the offset distance of the prismatic joint. Two special cases are illustrated with four and five bars. Examples are given to demonstrate the presented method able to cover all the cases of N-bar linkages with one or a set of adjoined prismatic joints and N-bar open-loop robotic mechanisms.

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Type Synthesis of Kinematically Redundant 3T1R Parallel Manipulators

Volume 6A: 37th Mechanisms and Robotics Conference ◽

10.1115/detc2013-12575 ◽

2013 ◽

Cited By ~ 1

Author(s):

Xianwen Kong ◽

Damien Chablat ◽

Stéphane Caro ◽

Jingjun Yu ◽

Clément Gosselin

Keyword(s):

Degrees Of Freedom ◽

Parallel Manipulators ◽

Parallel Mechanisms ◽

Type Synthesis ◽

Singular Configurations ◽

Revolute Joints ◽

Solid Foundation ◽

Moving Platform ◽

Forward Kinematic ◽

Open Issues

A kinematically redundant parallel manipulator (PM) is a PM whose degrees-of-freedom (DOF) are greater than the DOF of the moving platform. It has been revealed in the literature that a kinematically redundant PM has fewer Type II kinematic singular configurations (also called forward kinematic singular configurations, static singular configurations or parallel singular configurations) and/or constraint singular configurations than its non-redundant counterparts. However, kinematically redundant PMs have not been fully explored, and the type synthesis of kinematically redundant PMs is one of the open issues. This paper deals with the type synthesis of kinematically redundant 3T1R PMs (also called SCARA PMs or Schoenflies motion generators), in which the moving platform has four DOF with respect to the base. At first, the virtual-chain approach to the type synthesis of kinematically redundant parallel mechanisms is recalled. Using this approach, kinematically redundant 3T1R PMs are constructed using several compositional units with very few mathematical derivations. The type synthesis of 5-DOF 3T1R PMs composed of only revolute joints is then dealt with systematically. This work provides a solid foundation for further research on kinematically redundant 3T1R PMs.

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