Kinematic Analysis and Verification of a New 5-DOF Parallel Mechanism

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analyses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of five dimensions of freedoms including three-dimensional movement and two-dimensional rotation. Based on this, the real mechanism is built, but unfortunately it is found unstable in some positions. Grassmann line geometry method is applied to analyze its unstable problem caused by singular posture, and then an improving method is put forward to solve it. With the improved mechanism, closed loop vector method is employed to establish the inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get the mapping relationships between position, speed, and acceleration of moving and fixed platform. Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing factors of workspace, and then to get the better workspace. Finally, an experiment is designed to verify the mechanism working performance.

Study of a New 5-DOF Parallel Mechanism for Multi-Directional 3D Printing

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU for multi-directional 3D printing, and then analyses its DOF by traditional Grubler-Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of 5 dimensions of freedoms including three-dimensional movement and two-dimensional rotation. Basing on this, the real mechanism is built, but unfortunately it is found unstable in some positions. Grassmann line geometry method is applied to analyze its unstable problem caused by singular posture, and then an improving method is put forward to solve it. With the improved mechanism, closed loop vector method is employed to establish the inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get the mapping relationships between position, speed and acceleration of moving and fixed platform, Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing factors of workspace, and then to get the better workspace. Finally an experiment is designed to verify the mechanism working performance to satisfy the spatial motion requirements of multi-directional 3D printing.

A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Mobility, Singularity, and Kinematics Analyses of a Novel Spatial Parallel Mechanism

A spatial parallel kinematic mechanism (PKM) with five degrees of freedom (DoFs) and three limbs is proposed in this paper. To investigate the characteristics of the proposed mechanism's DoFs, mobility analysis based on a line graph method and Grassmann line geometry is carried out. The results show that the mobile platform can rotate about a fixed point at the base and translate in a specific plane (i.e., three rotations and two translations). Therefore, the mobile platform can be located at an arbitrary point in the space and has flexible orientational capability. The orientation of the mobile platform is described by using tilt-and-torsion (T&T) angles, and the kinematics model is established with this precondition. Within the process of kinematics modeling, parasitic motion of the mobile platform is analyzed, and singularity configurations are also disclosed. On this basis, four working modes with different configurations are identified, and one of them is focused on and investigated in detail. The proposed PKM has good potential to be used in the development of movable machine centers. The kinematic analysis is very helpful for the understanding of the concept and the potential applications.

Design of a new gravity balanced parallel mechanism with Schönflies motion

In this paper, a new gravity-balanced 3T1R parallel mechanism is addressed. Firstly, structure description, inverse and forward kinematic modeling are performed in detail. Secondly, Jacobian derivation based on screw theory and singularity analysis using Grassmann Line Geometry is performed, and then optimal kinematic design with respect to workspace size, kinematic isotropy and maximum force transmission ratio are conducted. Thirdly, the gravity balancing design using both counterweights and springs is proposed and a prototype of this mechanism is also presented. Results of analysis show that the proposed mechanism has quite a few potential applications.

Combinatorial Method for Characterizing Singular Configurations in Parallel Mechanisms

The paper presents a method for finding the different singular configurations of several types of parallel mechanisms/robots using the combinatorial method. The main topics of the combinatorial method being used are: equimomental line/screw, self-stresses, Dual Kennedy theorem and circle, and various types of 2D and 3D Assur Graphs such as: triad, tetrad and double triad. The paper introduces combinatorial characterization of 3/6 SP and compares it to singularity analysis of 3/6 SP using Grassmann Line Geometry and Grassmann-Cayley Algebra. Finally, the proposed method is applied for characterizing the singular configurations of more complex parallel mechanisms such as 3D tetrad and 3D double-triad.

Development of a novel two-limbed parallel mechanism having Schönflies motion

This paper introduces a novel parallel mechanism having Schönflies motion. The mechanism consists of only two RRPaR-type limbs. After a short description of its structure, its position analysis is conducted and its screw-based kinematic model is derived. Next, its singularity analysis is performed via Grassmann line geometry and then its optimal kinematic characteristics are examined with respect to workspace size and isotropy property. The results show that the proposed parallel mechanism has a very high potential to be used as a manipulator or a haptic device. A prototype of this mechanism was developed and tested to corroborate its performance.

Design of a novel 3-DoF parallel kinematic mechanism: type synthesis and kinematic optimization

SUMMARYThis paper deals with the design of a three-degree-of-freedom (3-DoF) parallel kinematic mechanism (PKM) with high orientational capability. First, a type synthesis method based on Grassmann line geometry and a line-graph method is proposed, and a novel 3-DoF PKM is derived based on this method. Thereafter, the parasitic motions of the derived mechanism are identified under two different orientation description methods, i.e., Tilt-and-Torsion angles (T&T angles) and Roll-Pitch-Yaw angles (RPY angles), and the kinematic optimization considering the motion/force transmissibility is carried out. On this basis, the orientational capability of the discussed mechanism is investigated, and the high orientational capability is demonstrated. The design of the 3-DoF PKM in this paper is very meaningful to the development of the five-axis machine tools with hybrid architectures. The design methods of type synthesis and kinematic optimization can also be used in the design of other PKMs.

Parallel singularity-free design with actuation redundancy: A case study of three different types of 3-degree-of-freedom parallel mechanisms with redundant actuation

Typical parallel mechanisms suffer from parallel singularity due to kinematic coupling of multichains. This paper investigates how to remove parallel singularities by using redundant actuations. First, actuation wrenches and constraint wrenches forming the full direct kinematic Jacobian matrix are derived. After briefly addressing conditions for their constraint singularities, Grassmann–Cayley algebra is employed to identify parallel singularities. Then, employing Grassmann line geometry, the locations and the minimum number of redundant actuators are identified for the parallel mechanisms to have parallel singularity-free workspace. Three different types of 3-degree-of-freedom parallel mechanisms such as planar, spherical, and spatial parallel mechanisms are given as exemplary devices.