Compositional Submanifolds of Prismatic–Universal–Prismatic and Skewed Prismatic–Revolute– Prismatic Kinematic Chains and Their Derived Parallel Mechanisms

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Xinsheng Zhang ◽  
Pablo López-Custodio ◽  
Jian S. Dai
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Planar Motion ◽  
Helical Motion ◽  
Parallel Mechanisms ◽  
Motion Group ◽  
Revolute Joint ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Joint Axis

The kinematic chains that generate the planar motion group in which the prismatic-joint direction is always perpendicular to the revolute-joint axis have shown their effectiveness in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the standard prismatic–revolute–prismatic (PRP) kinematic chain generating the planar motion group to a relatively generic case, in which one of the prismatic joint-directions is not necessarily perpendicular to the revolute-joint axis, leading to the discovery of a pseudo-helical motion with a variable pitch in a kinematic chain. The displacement of such a PRP chain generates a submanifold of the Schoenflies motion subgroup. This paper investigates for the first time this type of motion that is the variable-pitched pseudo-planar motion described by the above submanifold. Following the extraction of a helical motion from this skewed PRP kinematic chain, this paper investigates the bifurcated motion in a 3-prismatic–universal–prismatic (PUP) parallel mechanism by changing the active geometrical constraint in its configuration space. The method used in this contribution simplifies the analysis of such a parallel mechanism without resorting to an in-depth geometrical analysis and screw theory. Further, a parallel platform which can generate this skewed PRP type of motion is presented. An experimental test setup is based on a three-dimensional (3D) printed prototype of the 3-PUP parallel mechanism to detect the variable-pitched translation of the helical motion.

Product Submanifold Based Analysis of Kinematic Chains and a 3-PUP Parallel Mechanism

2016 ◽  
Author(s):  
Xinsheng Zhang ◽  
Jian S. Dai
Keyword(s):  
Lie Group ◽  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Planar Motion ◽  
Motion Group ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Screw Motion ◽  
Joint Axis ◽  
Joint Direction

The five types of kinematic chains that generate the planar motion group SE(2) of dimension three, with the prismatic-joint direction always perpendicular with the revolute-joint axis in each chain, have shown their effectiveness and manifested the charm in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the traditional PRP kinematic chain generating the planar motion group SE(2) to a relatively general case, in which one of the prismatic joint-direction is not necessarily perpendicular with the revolute-joint axis, leading to the discovery of a screw motion with a variable pitch in this kinematic chain. Following the extraction of a screw motion from this particular PRP kinematic chain, this paper presents the bifurcated motion in a 3-PUP parallel mechanism by changing the active geometrical constraint in its configuration space, with a Lie group approach and interpretation. The constraint-singularity configuration sets for bifurcation of the 3-PUP parallel mechanism. The paper hence provides a Lie group representation and geometry interpretation for the kinematic equivalence of serial chains and the bifurcated motion of a parallel mechanism.

scholarly journals Design of Self-Reconfigurable Multiarm Robot Mechanism Based on Deployable Kinematic Chains

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Fu-Qun Zhao ◽  
Sheng Guo ◽  
Hai-Jun Su ◽  
Hai-Bo Qu ◽  
Ya-Qiong Chen
Keyword(s):  
Parallel Mechanism ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
Assembly Method ◽  
Operation Modes ◽  
Object Based ◽  
Switch Operation ◽  
Storage Area ◽  
Mechanism Theory

Abstract As the structures of multiarm robots are serially arranged, the packaging and transportation of these robots are often inconvenient. The ability of these robots to operate objects must also be improved. Addressing this issue, this paper presents a type of multiarm robot that can be adequately folded into a designed area. The robot can achieve different operation modes by combining different arms and objects. First, deployable kinematic chains (DKCs) are designed, which can be folded into a designated area and be used as an arm structure in the multiarm robot mechanism. The strategy of a platform for storing DKCs is proposed. Based on the restrictions in the storage area and the characteristics of parallel mechanisms, a class of DKCs, called base assembly library, is obtained. Subsequently, an assembly method for the synthesis of the multiarm robot mechanism is proposed, which can be formed by the connection of a multiarm robot mechanism with an operation object based on a parallel mechanism structure. The formed parallel mechanism can achieve a reconfigurable characteristic when different DKCs connect to the operation object. Using this method, two types of multiarm robot mechanisms with four DKCs that can switch operation modes to perform different tasks through autonomous combination and release operation is proposed. The obtained mechanisms have observable advantages when compared with the traditional mechanisms, including optimizing the occupied volume during transportation and using parallel mechanism theory to analyze the switching of operation modes.

scholarly journals Reconfiguration Analysis of a 3-DOF Parallel Mechanism

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
The Third ◽  
Equilateral Triangles ◽  
Moving Platform

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

The Manta and the Kanuk: Novel 4-DOF Parallel Mechanisms for Industrial Handling

1999 ◽  
Author(s):  
Luc H. Rolland
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Parallel Robot ◽  
Chain Structure ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Low Mass ◽  
Loading And Unloading ◽  
Very High

Abstract Two novel 4-DOF very fast parallel robots were designed. This paper introduces the new parallel mechanism designs which are named the Manta and the Kanuk. In order to reduce manipulator overall costs, the actuator and encoder numbers are minimized to the exact effective degrees-of-freedoms (DOF) which is usually not the case in most parallel robot designs. The robots allow end-effector displacements along the three Cartesian translations and one platform transversal rotation. The two remaining rotations are blocked by the intrinsic mechanical structure including the rotation along the platform normal which is always limited in range. The main advantages are high stiffness through the multiple kinematic chain structure which allow for low mass designs. Moreover, they feature simple mechanical construction. Thus, it shall be possible to achieve very high throughput since high accelerations are feasible. To circumvent the known workspace limitations, the actuators were selected to be prismatic along linear axes. The applications are automated warehouse manipulation, mediatheque manipulation, machine tool tool changers, loading and unloading.

Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Ketao Zhang ◽  
Jian S. Dai ◽  
Yuefa Fang
Keyword(s):  
Phase Change ◽  
Unique Feature ◽  
Kinematic Chain ◽  
Geometric Constraint ◽  
Parallel Mechanisms ◽  
Geometrical Condition ◽  
Revolute Joint ◽  
Underlying Principle ◽  
Source Phase ◽  
Hooke’S Joint

This paper presents a unique feature of geometric constraint of adjacent axes of the variable-axis (vA) joint and analyses the effectiveness in the constructed limb, resulting in variation of mobility configuration of two 3SvPSv metamorphic parallel mechanisms. The underlying principle of the metamorphosis of this vA joint is unravelled by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the vA joint from the source phase Sv to the variable Hooke’s joint phase Uv and the variable revolute-joint phase Rv. The kinematic chain installed with the vA joint forms a reconfigurable limb and is then used to construct two 3SvPSv metamorphic parallel mechanisms proposed in this paper. The phase change of the vA joints incurs the constraint change of the SvPSv limb and subsequently results in the change of mobility configuration of the metamorphic parallel mechanisms. The paper further addresses the geometrical condition for constructing 3SvPSv metamorphic parallel mechanisms following the constraints delivered by the reconfigurable limbs, leading to the analysis of mobility change of the mechanisms induced by the phase change of the limbs.

Mobility Analysis of a Novel 3-5R Parallel Mechanism Family

2004 ◽  
Vol 126 (1) ◽  
pp. 79-82 ◽  
Author(s):  
Q. C. Li ◽  
Z. Huang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

Mobility analysis of a novel 3-5R parallel mechanism family whose limb consists of a 2R and a 3R parallel subchain is performed by the aid of screw theory. A mobility criterion applicable to such 3-leg parallel mechanisms in which each kinematic chain contains five kinematic pairs is proposed. It is shown that under different structural conditions, the 3-5R parallel mechanism can have 3, 4, or 5 DOF (degrees of freedom). The structural conditions that guarantee the full-cycle mobility are analyzed. The analysis and the method presented in this paper will be helpful in using such a 3-5R parallel mechanism family and introduce new insights into the mobility analysis of parallel mechanisms.

Dexterous Workspace of n-PRRR Planar Parallel Manipulators

2012 ◽  
Vol 4 (3) ◽  
Author(s):  
André Gallant ◽  
Roger Boudreau ◽  
Marise Gallant
Keyword(s):  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Divergence Theorem ◽  
End Effector ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Planar Surfaces ◽  
Revolute Joints ◽  
Gauss Divergence Theorem ◽  
Planar Parallel Manipulators

In this work, a method is presented to geometrically determine the dexterous workspace boundary of kinematically redundant n-PRRR (n-PRRR indicates that the manipulator consists of n serial kinematic chains that connect the base to the end-effector. Each chain is composed of two actuated (therefore underlined) joints and two passive revolute joints. P indicates a prismatic joint while R indicates a revolute joint.) planar parallel manipulators. The dexterous workspace of each nonredundant RRR kinematic chain is first determined using a four-bar mechanism analogy. The effect of the prismatic actuator is then considered to yield the workspace of each PRRR kinematic chain. The intersection of the dexterous workspaces of all the kinematic chains is then obtained to determine the dexterous workspace of the planar n-PRRR manipulator. The Gauss divergence theorem applied to planar surfaces is implemented to compute the total dexterous workspace area. Finally, two examples are shown to demonstrate applications of the method.

Coupling Degree of Mechanism and Its Application

2006 ◽  
Author(s):  
Jing Xiong ◽  
Ting-Li Yang ◽  
Xiangdong Yang ◽  
Dongchao Yang ◽  
Ken Chen
Keyword(s):  
Dynamic Analysis ◽  
Topological Structure ◽  
Parallel Mechanism ◽  
Kinematics And Dynamics ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
Unified Modeling

The kinematic and dynamic analysis of an spatial multi-loop mechanism especially parallel mechanism is significant but always complex. Based on the topological structure of mechanisms, this paper proposes the concept of coupling degree of mechanism systematically, and applies it to the criterion of basic kinematic chains(BKCs) and other problems. The relation between topology, kinematics and dynamics of parallel mechanisms is established, and then it is achieved to quantitatively describe the analysis complexity of a parallel mechanism and to obtain its simplest solving path, according to its topological structure. The preliminary method for unified modeling of the topology, kinematics and dynamics of parallel mechanisms is proposed, using BKC as the basic analysis unit. Some suggestions for optimization and selective preference of parallel mechanisms are also presented.

Workspace Analysis of a Novel Six-Degrees-of-Freedom Parallel Manipulator With Coaxial Actuated Arms

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Mats Isaksson ◽  
Matthew Watson
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Limited Range ◽  
Parallel Mechanisms ◽  
Six Degrees Of Freedom ◽  
Serial Robots ◽  
High Acceleration ◽  
Redundantly Actuated

Parallel manipulators possess several advantages compared to serial robots, including the possibilities for high acceleration and high accuracy positioning of the manipulated platform. However, the majority of all proposed parallel mechanisms suffer from the combined drawbacks of a small positional workspace in relation to the manipulator footprint and a limited range of rotations of the manipulated platform. This paper analyses a recently proposed six-degrees-of-freedom parallel mechanism that aims to address both these issues while maintaining the traditional advantages of a parallel mechanism. The investigated manipulator consists of six actuated coaxial upper arms that are allowed to rotate indefinitely around a central cylindrical base column and a manipulated platform where five of the six joint positions are collinear. The axis-symmetric arm system leads to an extensive positional workspace while the proposed link arrangement increases the range of achievable platform rotations. The manipulator workspace is analyzed in detail and two methods to further increase the rotational workspace are presented. It is shown that the proposed manipulator has the possibility of a nonsingular transition of assembly modes, which extends the usable workspace. Furthermore, it is demonstrated how an additional kinematic chain can be utilized to achieve infinite platform rotation around one platform axis. By introducing additional mobility in the manipulated platform, a redundantly actuated mechanism is avoided.

Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain

2005 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Second Step ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Serial Chain ◽  
Parallel Kinematic

This paper presents a systematic approach for the mobility analysis of parallel mechanisms. The method is based on screw theory and the concept of equivalent serial chain. An equivalent serial kinematic chain of a k-legged PKC (parallel kinematic chain) is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. Using the proposed approach, the mobility analysis of a PKC is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step is dealt with based on screw theory. The second step is performed with the aid of the concept of equivalent serial chain and the types of multi-DOF overconstrained single-loop kinematic chains. The proposed approach is illustrated with several examples.

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