Xianwen Kong

Type synthesis of 3-DOF spherical parallel manipulators based on screw theory

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time.

Type synthesis of 3-DOF translational parallel manipulators based on screw theory

A method is proposed for the type synthesis of 3-DOF (degree-of-freedom) translational parallel manipulators (TPMs) based on screw theory. The wrench systems of a translational parallel kinematic chain (TPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of TPMs. The type synthesis of legs for TPKCs, the type synthesis of TPKCs as well as the selection of actuated joints of TPMs are dealt with in sequence. An approach to derive the full-cycle mobility conditions for legs for TPKCs is proposed based on screw theory and the displacement analysis of serial kinematic chains undergoing small joint motions. In addition to the TPKCs proposed in the literature, TPKCs with inactive joints are synthesized. The phenomenon of dependent joint groups in a TPKC is revealed systematically. The validity condition of actuated joints of TPMs is also proposed. Finally, linear TPMs, which are TPMs whose forward displacement analysis can be performed by solving a set of linear equations, are also revealed.

Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory

3T1R four-degrees-of-freedom (DOF) parallel manipulators (3T1R-PMs) are the parallel counterparts of the 4-DOF SCARA serial robots. In a 3T1R-PM, the moving platform can generate 3T1R motion (also called Schonflies motion), which refers to a rotation about any axis with a given direction in conjunction with 3-DOF translations. A method is proposed for the type synthesis of 3T1R-PMs based on screw theory. The wrench systems of a 3T1R parallel kinematic chain (3T1R-PKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of 3T1R-PMs. The type synthesis of legs for 3T1R-PKCs, the type synthesis of 3T1R-PKCs, as well as the selection of actuated joints of 3T1R-PMs, are dealt with in sequence. 3T1R-PKCs with and without inactive joints are synthesized. The phenomenon of dependent joint groups in a 3T1R-PKC is revealed for the first time. Several 3T1R-PMs with identical type of legs are obtained.

Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator:

A new three-degrees-of-freedom (3-DOF) translational parallel manipulator (TPM) with linear actuators, i.e., 3-CRR TPM, is first proposed. The rotation singularity analysis, the inverse kinematics, the forward kinematics, and the kinematic singularity analysis of the 3-CRR TPM are then performed. The analysis shows that the proposed TPM has the following kinematic merits over previous TPMs. (1) The forward displacement analysis can be performed by solving a set of linear equations. (2) The Jacobian matrix of the TPM is constant. The inverse of the Jacobian matrix can be pre-calculated, and there is no need to calculate repeatedly the inverse of the Jacobian matrix in performing the forward displacement analysis and forward velocity analysis. (3) There is no rotation singularity. (4) There is no uncertainty singularity. (5) The TPM has a fewer number of links or joints. The geometric condition for a 3-CRR TPM to be isotropic is also revealed. Two additional kinematic merits exist for the isotropic 3-CRR TPM. The first is that an isotropic 3-CRR TPM is isotropic in its whole workspace. The second is that no calculation is needed in order to pre-determine the inverse of the Jacobian matrix. Finally, preliminary design considerations are presented.

Type Synthesis of Three-Degree-of-Freedom Spherical Parallel Manipulators

A spherical parallel manipulator (also called an orientational parallel manipulator or rotational parallel manipulator) refers to a threedegreeof-freedom (3-DoF) parallel manipulator in which the moving platform undergoes a 3-DoF spherical motion or rotates about a fixed point. In this paper, we propose a new method for the type synthesis of non-overconstrained (isostatic) spherical parallel manipulators. In a non-overconstrained three-legged spherical parallel manipulator, each leg is composed of five revolute, prismatic and/or helical joints. Using the proposed approach, non-overconstrained three-legged spherical parallel manipulators can be obtained by the combination of a 3-RRR overconstrained spherical parallel manipulator and three four-bar Delassus linkages with at least one revolute joint. In a 3-RRR spherical parallel manipulator, each leg is composed of three revolute joints whose axes pass through the center of spherical motion. A four-bar Delassus linkage is a single-DoF four-bar linkage composed of four revolute, prismatic and/or helical joints. A number of new non-overconstrained spherical parallel manipulators are also identified, including one obtained by the combination of a 3-RRR spherical parallel manipulator and three Bennett linkages.

Type Synthesis of Linear Translational Parallel Manipulators

Linear TPMs (3-leg 3-DOF translational parallel manipulators) refer to TPMs whose forward displacement analysis can be performed by solving a set of linear equations. A method is proposed for the type synthesis of linear TPMs. The proposed method is based on the geometric interpretation of the forward displacement analysis and the fact that the intersection of three planes can be obtained by solving a set of linear equations. Then, all linear TPMs are obtained. Finally, all I-O (input-output) decoupled linear TPMs are revealed. An I-O decoupled linear TPM refers to a linear TPM for which three translations of the moving platform along three orthogonal directions can be controlled independently by three actuators.

Type Synthesis of Parallel Mechanisms With Multiple Operation Modes

There are usually several motion patterns having the same degrees of freedom (DOF). For example, planar motion, spherical motion, and spatial translation are motion patterns with 3 DOF. An f-DOF parallel mechanism with multiple operation modes is a parallel mechanism that can generate different motion patterns with f DOF. Up to now, no method has been proposed for the type synthesis of parallel mechanisms with multiple operation modes. This paper presents a general method for the type synthesis of parallel mechanisms with multiple operation modes. Using the proposed approach, 3-DOF parallel mechanisms with both spherical and translational modes, i.e., parallel mechanism generating both a spherical motion pattern and a spatial translational motion pattern, are generated systematically. A large number of parallel mechanisms with both spherical and translational modes are obtained.

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

A four-decree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schonflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations, and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using, an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

Type synthesis of 3-DOF PPR-equivalent parallel manipulators based on screw theory and the concept of virtual chain

PPR-equivalent parallel manipulators (PMs) are a class of 3-DOF PMs with great application potential. They are indeed the parallel counterparts of the 3-DOF PPR serial robots, in which the moving platform can rotate arbitrarily about an axis undergoing a planar translation. This paper deals with the type synthesis of 3-DOF PPR-equivalent PMs. At first, virtual chains are introduced to represent the motion patterns of 3-DOF motions and relevant results from screw theory are recalled. A method is then proposed for the type synthesis of 3-DOF PPR-equivalent PMs. Using the proposed approach, the type synthesis of 3-DOF PPR-equivalent PMs is performed in three steps. In addition to all the 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs proposed in the literature, a number of new 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs are identified. It is also found that there are no PPR-equivalent PMs with identical type of legs. The type synthesis of PPR-equivalent PMs is well solved using the proposed approach. The characteristic of the proposed approach is that the type synthesis of PPR-equivalent parallel kinematic chains is reduced to the type synthesis of 3-DOF single-loop kinematic chains and thus easy to perform.

A Novel Large-Range XY Compliant Parallel Manipulator With Enhanced Out-of-Plane Stiffness

There is an increasing need for compact large-range XY compliant parallel manipulators (CPMs). This paper deals with a novel large-range XY CPM with enhanced out-of-plane stiffness (LRXYCPMEOS). Unlike most of XY CPMs based on the 4-PP (P: prismatic) decoupled parallel mechanism, the LRXYCPMEOS is obtained from a 4-PP-E (E: planar) decoupled parallel mechanism by replacing each P joint with a planar double multibeam parallelogram module (DMBPM) and the E joint with a spatial double multibeam parallelogram module. Normalized analytical models for the LRXYCPMEOS are then presented. As a case study, an LRXYCPMEOS with a motion range 10 mm × 10 mm in both positive directions is presented in detail, covering the geometrical parameter determination, performance characteristics analysis, actuation force check, and buckling check. The analytical models are compared with the finite element analysis (FEA) models. Finally, dynamics consideration, manufacturability, out-of-plane stiffness, and result interpretation are discussed. It is shown that the LRXYCPMEOS in the case study has the following merits: large range of motion up to 20 mm × 20 mm, enhanced out-of-plane stiffness which is approximately 7.1 times larger than the associated planar XY CPM without the spatial compliant leg, and well-constrained parasitic motion with the parasitic translation along the Z-axis less than 2 × 10−4 mm, the parasitic rotation about the X-axis/Y-axis less than 2 × 10−6 rad, and the parasitic rotation about the Z-axis below 1 × 10−6 rad.