Geometry and Constraint Based Design of Metamorphic Parallel Mechanisms

This paper presents a unique feature of geometric and physical constraint of axes of the reconfigurable-axis (rA) joint and analyses the effectiveness in the constructed limb, resulting in variation of mobility configuration of metamorphic parallel mechanism. This change in mobility is completed by two cases illustrated by a 3(rA)PS metamorphic parallel mechanism having variable mobility from 3 to 6. The underlying principle of the metamorphosis of this rA joint is demonstrated by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the rA joint from the two types of spherical joints to the three types of variable Hooke joints and the one revolute joint. This new type of metamorphic parallel mechanism has broad application prospects, especially in the field of 3d printing. According to the complexity of the shape of the workpiece, the degree of freedom corresponding to different topologies can be selected, which can reduce the costs and increase the adaptability to different working conditions.

A parallelogram allows the output link to remain at a fixed orientation with respect to an input link, for which it acts as a unique role in the design of parallel mechanisms. In this paper, the unique role of a parallelogram is used completely to design some new parallel mechanisms with two to six degrees of freedom (DoFs). In these mechanisms, some with three DoFs possess the advantage of very high rotational capability and some with two DoFs have the translational output of a rigid body. More than that, the design concept is also applied first to some parallel mechanisms to improve the systems' rotational capability. The parallel mechanisms proposed in this paper have wide applications in industrial robots, simulators, micromanipulators, parallel kinematics machines, and any other manipulation devices in which high rotational capability and stiffness are needed. Especially, the paper provides new concepts of the design of novel parallel mechanisms and the improvement of rotational capability for such systems.

Topology design of (3T-1R) parallel mechanism (PM) based on POC equations is discussed in detail as an example to illustrate the systematic method for topology design of PMs proposed in Chap. 9. The design process includes two stages. The first stage involves traditional structure synthesis, which results in 18 structure types of (3R-1R) PMs that contain no P pairs. The second stage includes topological performance analysis and classification of the obtained PM structure types which may help designer to select the most suitable structure type. Its core contents include: (1) Key steps of topology design for (3R-1R) PMs include: (a) Determine structure types of the SOC branch containing only R and P pairs according to the method for structure synthesis of SOC branch described in Chap.8. Then obtain corresponding HSOC branches through topologically equivalent principle in Chap.9. (b) Determine the geometrical condition for assembling branches between two platforms according to corresponding basic formulas in Chap. 9. Then determine different assembling schemes for the same geometrical condition. (c) Performance analysis and classification of the obtained PM structures are conducted based on topological characteristics of PMs in Chap. 9. The result can be used for assessment and optimization of (3R-1R) PM structure types. (2) 18 types of (3T-1R) PM structures containing no P pair are obtained, two of which have already been used in existing SCARA parallel robots. The other structure types may potentially be used in new SCARA parallel robots. (3) These 18 structure types of (3R-1R) PMs are classified into four types: Type-1 include four PMs containing only SOC branches; Type-2 include six PMs containing only HSOC branches; Type-3 include seven PMs containing both HSOC and SOC branches; Type-4 include three PMs with partial motion decoupling property. (4) According to topological performance analysis and classification of these PMs based on topological characteristics, the type-3 PM has a higher rigidity than a type-1 PM and a larger workspace than a type-2 PM. So, special attentions shall be paid to type-3 PMs.

Traditional bionic joints including wrist, waist, ankle and shoulder have three revolute degrees of freedom, which can be treated as spherical joints, and its structure is prone to be damaged with impact force through the center of spherical joint. In this paper, a novel metamorphic parallel mechanism with two configurations used for bionic joint design is presented. The origin kinematic chain for this metamorphic mechanism, which is also the first configuration mechanism, consists of a moving platform, a base plate and four connecting legs between moving platform and base plate. In contrast with traditional ankle joint, a constrained translational degree of freedom can be activated in origin kinematic chain to avoid impact damage. The origin kinematic chain can transform to the second configuration mechanism which is in possession of three revolute degrees of freedom and equivalent to normal spherical joint. The transforming process is represented by new incidence matrix and the motion characteristics of this metamorphic mechanism in different configuration corresponding to each work-stage are analysed using screw theory.

Multiple bifurcated reconfiguration of double-loop metamorphic mechanisms with prismatic joints

The parallel mechanism exhibits high stiffness and excellent dynamic response, making it ideal for high-precision applications. In our early work, a novel 6-DOF redundant parallel posture mechanism with four limbs for solar wing docking has been proposed; each limb consists of three links and four joints. This paper primarily focuses on optimization design of the mechanism. The calculation of workspace volume reveals that factors influencing the range of posture adjustment include dynamic platform parameters, static platform parameters, the drive trajectory of each kinematic pair, and the angles between each kinematic pair. A sensitivity analysis was conducted to examine the impact of each parameter on the range of posture adjustment. To reduce computational complexity and improve analysis efficiency, a combined approach of single-factor analysis and response surface methodology (RSM) is used in the paper. Single-factor analysis is utilized to evaluate the effect of each parameter on the posture adjustment range. Based on these results, RSM is used to establish a regression model for parameters; thereby, the optimal parameter combination for the mechanism is determined. The regression coefficient R2 = 0.9374 attests to the validity of the proposed model. Finally, a comparison of the posture adjustment range before and after optimization is presented, providing a foundation for the practical application of the redundant parallel mechanism. This paper introduces a novel structural design concept aimed at resolving the conflict between heavy loads and compact sizes in redundant parallel mechanisms while providing valuable insights for miniaturized design.

This paper introduced a new metamorphic parallel mechanism consisting of four reconfigurable rTPS limbs. Based on the reconfigurability of the reconfigurable Hooke (rT) joint, the rTPS limb has two phases while in one phase the limb has no constraint to the platform, in the other it constrains the spherical joint center to lie on a plane. This results in the mechanism to have ability of reconfiguration between different topologies with variable mobility. Geometric constraint equations of the platform rotation matrix and translation vector are set up based on the point-plane constraint, which reveals the bifurcated motion property in the topology with mobility 2 and the geometric condition with mobility change in altering to other mechanism topologies. Following this, a unified kinematics limb modeling is proposed considering the difference between the two phases of the reconfigurable rTPS limb. This is further applied for the mechanism modeling and both the inverse and forward kinematics is analytically solved by combining phases of the four limbs covering all the mechanism topologies.

In this paper, we focus on a 6-DOF parallel mechanism which is for human hip joint power assist. Different from the conventional power assist system, the proposed human hip joint assisting mechanism is formed as parallel mechanism. Considering the anatomical mechanism of human hip joint, the 6-DOF assisting system consists of three serial chains, and each chain is a UPS model, so the parallel mechanism is a 3-UPS model. Based on the analysis the direct kinematic Jacobian of the parallel mechanism and human thigh, such a parallel mechanism design could be effectively used to hip joint power assist. This parallel assisting mechanism could be used for human thigh movement assisting, rehabilitation and movement information acquiring.

Design of hip joint assistant asymmetric parallel mechanism and optimization of singularity-free workspace

A computer-aided geometry approach for solving type design and performance analysis of 4-DOF parallel mechanism is put forward. By using the geometric constraint, the dimension constraint, the dimension equation and the dimension driving techniques of CAD, some simulation mechanisms of the novel 4-DOF parallel robot are created. When the driving dimensions of driving limbs are modified, the configuration of the simulation mechanisms are varied correspondingly, and the kinematic parameters of the moving platform are solved. The equation of forward and inverse displacement is established by the analytical result. The results of computer simulation prove that the computer aided geometric approach is not only fairly quick and straightforward, but also has the advantages of accuracy and repeatability. It also can conducted kinematic analysis of spatial parallel mechanisms without complicated analytics and program.

When limbs of a parallel mechanism have been selected, the geometric relation among limbs determines the mechanism's motion. The limb arrangement which affects the mechanism's motion raises a fundamental and significant issue. If a mechanism only owns limbs with Lie group motions, it is convenient to predict how a limb arrangement determines the mechanism's motion. However, if a mechanism is mainly or purely constituted by limbs with motions of general differential manifolds, it is difficult to find the influence of a limb arrangement. On this regard, this paper provides an in-depth investigation by focusing on motion analysis of parallel mechanisms consisting of three PRS limbs with planar-spherical manifolds. By formulating and comparing the motion characteristics of these mechanisms which though could be modeled difficultly by a mathematical tool without using the finite displacement screw, a finite displacement screw-based group method is proposed in this paper to resolve the raised issue. The novel approach presents results in expressions of new types of manifold motions, providing a foundation for design and application of parallel mechanisms having the various three-planar-spherical manifolds’ intersection motions.

Global Stiffness design and optimization of parallel mechanisms can be a difficult and time-consuming exercise in parallel robot design, especially when the variables are multifarious and the objective functions are too complex. To address this issue, optimization techniques based on kinetostatic model and genetic algorithms are investigated as the effective criteria. First, a 5-DOF parallel mechanism with a passive constraining leg and five identical legs with prismatic actuators for machine tool is proposed, and its corresponding inverse kinematics, Jacobian matrices and global velocity equation are derived. Second, with the kinetostatic model, the mean value and the standard deviation of the trace of the global compliance distribution are proposed as these two kinetostatic performance indices. Finally, the effectiveness of this optimization design methodology for global stiffness indices is validated with simulation.

This paper deals with the kinematics and analysis of a new parallel mechanism with a suspended platform. The proposed mechanism has a unique appearance in that the 6 chains originating from a circular ring are connected to the both ends of a suspended platform. After introducing the kinematics, the architecture singularity problem is analyzed. Then, the kinematic characteristics of this mechanism are analyzed with respect to the workspace and the isotropic index. Kinematic optimization of this mechanism was also performed. Finally, the proposed robot was employed as an automatic device for otologic surgery.

Aiming at the problem that the existing 2R1T (two rotations and one translation) vehicle engine motion simulation platform mechanism cannot realistically simulate the motion state of the engine due to the parasitic motion. In this paper, the geometric relationship between the restraint force of the branch and the rotation axis of the 2R1T parallel mechanism(PM) is analyzed. A construction criterion of the branch for redundant mechanism without parasitic motion is proposed. From the perspective of mechanism innovation design, a novel 2-RPS/2-UPS/PS PM with large bearing capacity without parasitic motion is designed. This paper solves the problem that the existing 2R1T PM without parasitic motion cannot be applied to the occasion of large load. The kinematics analysis of the mechanism is carried out, and the characteristic of the mechanism without parasitic motion is verified. The workspace of the mechanism is calculated. And the kinematics simulation analysis, stress analysis and prototype experiment of the mechanism are carried out. The correctness of the design index of the motion simulation platform and the characteristic of the mechanism without parasitic motion is proved. It provides a theoretical basis for the application of the mechanism without parasitic motion in large load-bearing occasions.

Passive gravity compensation technologies based on counterweight and torsional springs is rarely discussed due to the unavailability of an exact mathematical manipulation to determine the required spring constants to achieve the static balance. This article proposes using these springs for a parallel kinematics mechanism with revolute joints. Either the spring constants or initial spring displacements are determined by a constrained optimization approach aiming at minimizing the total potential energy of the mechanism or the static reaction in the actuation direction at theactuators, along a prescribed trajectory. This results in reduced actuation forces/ torques and hence reduced power consumption.