Screw Analysis, Modeling and Experiment on the Mechanics of Tibia Orthopedic with the Ilizarov External Fixator

The Ilizarov external fixator plays an important role in the correction of complex malformed limbs. Our purpose in this work was to reveal the transmission of adjustable forces between the external fixator and the broken bone, and express the stress distribution at the end of the broken bone during the orthopedic treatment. Firstly, the screw model of the fixator was established and the theoretical relationship between the adjustable force and the stress was obtained. A sheep tibia was taken as a representative research object and its ediTable 3D entity was obtained by CT scanning. Then the mechanical model of the fixator and tibia was built using the ABAQUS software. Correction experiments were performed on the sheep tibia to measure the adjustable/support forces and tensions of the tibia. The measured results were imported to the screw and mechanical model, and the theoretical and simulation values were calculated. The theoretical tensions calculated by the screw model had a similar shape and doubled the value compared with that of the measured results. The transfer efficiency between the two results was improved and kept at about 50% after the initial 2~3 periods. The maximum stress occurring at the surface of the broken bone end was near the Kirschner wire pinhole. The simulation results for the tensions from the mechanical model showed a similar change trend, and the value was slightly higher. A biomechanical model of the Ilizarov external fixator was derived and verified through calculations, simulations and experiments. The change law of the adjustable forces and the tensions existing in the broken sheep tibias is presented herein, and offers a helpful contribution to orthopedic treatment.

Type synthesis of legged mobile landers with one passive limb using the singularity property

During extraterrestrial planetary exploration programs, autonomous robots are deployed using a separate immovable lander and a rover. This mode has some limitations. In this paper, a concept of a novel legged robot with one passive limb and singularity property is introduced that has inbuilt features of a lander and a rover. Currently, studies have focused primarily on a performance analysis of the lander without a walking function. However, a systematic type synthesis of the legged mobile lander has not been studied. In this study, a new approach to the type synthesis used for the robot is proposed based on the Lie group theory. The overall concept and design procedures are proposed and described. The motion requirements of the robot and its legs, which are corresponding to the multi-function, are extracted and described. The layouts of the subgroups or submanifolds of the limbs are determined. The structures of the passive and actuated limbs are synthesized. Numerous structures of the legs with a passive limb are produced and listed corresponding to the desired displacement manifolds. Numerous novel structures of legs for the legged mobile lander are presented and listed. Then, four qualitative criteria or indexes are introduced. Based on the proposed criteria, a leg's configuration is selected as the best. A typical structure of the legged mobile lander is obtained by assembling the structures of the proposed legs. Finally, the typical robot is used as an example to verify the capabilities of the novel robot using a software simulation (ADAMS).

Position analysis, singularity loci and workspace of a novel 2PRPU Schoenflies-motion generator

Pick-and-place applications need to perform rigid body displacements that combine translations along three independent directions and rotations around one fixed direction (Schoenflies motions). Such displacements constitute a four-dimensional (4-D) subgroup (Schoenflies subgroup) of the 6-D displacement group. The four-degrees of freedom (dof) manipulators whose end effector performs only Schoenflies motions are named Schoenflies-motion generators (SMGs). The most known SMGs are the serial robots named SCARA. In the literature, parallel manipulators (PMs) have also been proposed as SMGs. Here, a novel single-loop SMG of type 2PRPU is studied. Its position analysis, singularity loci and workspace are addressed to provide simple analytic and geometric tools that are useful for the design. The proposed single-loop SMG is not overconstrained, its actuators are on or near the base and its end effector can perform a complete rotation. These features solve the main drawbacks that parallel SMG architectures have in general and make the proposed SMG a valid design alternative.

A simple and visually orientated approach for type synthesis of overconstrained 1T2R parallel mechanisms

This paper presents a simple and highly visual approach for the type synthesis of a family of overconstrained parallel mechanisms that have one translational and two rotational movement capabilities. It considers, especially, mechanisms offering the accuracy and dynamic response needed for machining applications. This family features a spatial limb plus a member of a class of planar symmetrical linkages, the latter connected by a revolute joint either to the machine frame at its base link or to the platform at its output link. Criteria for selecting suitable structures from among numerous candidates are proposed by considering the realistic practical requirements for reconfigurability, movement capability, rational component design and so on. It concludes that a few can simultaneously fulfil the proposed criteria, even though a variety of structures have been presented in the literature. Exploitation of the proposed structures and evaluation criteria then leads to a novel five degrees of freedom hybrid module named TriMule. A significant potential advantage of the TriMule over the Tricept arises because all the joints connecting the base link and the machine frame can be integrated into one single, compact part, leading to a lightweight, cost effective and flexible design particularly suitable for configuring various robotized manufacturing cells.

Control distribution of partially decoupled multi-level manipulators with five DOFs

Multi-level manipulators are those mechanisms in which two or more levels, that define the main chain of the manipulator, are joined in parallel to each other. Besides, each level is linked to the base in parallel by some limbs. Based on the idea of multi-level manipulators and using the concept of plain leg surfaces, the synthesis of partially decoupled manipulators with five degrees of freedom is presented. Among the different possibilities that exist to design the main chain of the manipulator, one is selected and the different manipulators that can be obtained from this option are analyzed. The concept of control distribution per level is presented and compared with the distribution of degrees of freedom per level. Finally, each of the proposed manipulators is studied and those which decouple the rotations are chosen.

Kinematics analysis and singularities of novel decoupled parallel manipulators with simplified architecture

Parallel manipulators (PMs) with decoupled kinematics can be obtained by combining a translational PM (TPM) with a spherical PM (SPM) either in multiplatform architectures or in integrated more-complex architectures. Some of the latter type are inspired by the 6–4 fully parallel manipulator (6–4 FPM), whereas others of the same type are deduced by suitably combining TPMs' limbs and SPMs' limbs into more cumbersome limbs which contain more than one actuated joint. The decoupled PMs (DPMs) presented here pursue an intermediate concept between the last two which keeps all the actuators on or near to the base in a simplified architecture with only three limbs. These features preserve the lightness of the mobile masses, together with the associated good-dynamic performances, and reduce the limitations on the workspace due to the eliminated limbs and to possible limb interferences. The finite and instantaneous kinematics of the proposed DPMs is studied, thus proving the practical implementation of the proposal.

Topology Synthesis of a 1-Translational and 3-Rotational Parallel Manipulator With an Articulated Traveling Plate

Driven by the increasing demands of the aircraft assemblage for the pose-adjustment equipment in the large-scale component docking, this paper carries out the topology synthesis of a 1-translational and 3-rotational (1T3R) four degrees of freedom (DoF) parallel manipulator with an articulated traveling plate. First, the articulated traveling plate is defined as that includes more than one rigid body articulated by one or more kinematic joints. Then, the relationship among the DoFs of the parallel manipulator and the articulated traveling plate and the number of the in-parts are proposed. According to the agreement of the arrangement way between the open-loop limbs and the in-parts, the topology synthesis procedure of the 1T3R 4-DoF parallel manipulator with an articulated traveling plate is proposed. Finally, their topology structures are obtained by discussing those of four types in terms of 1D-H, 1D-V type with opposite layout and 1D-H, 1D-V type with adjacent layout, in which the topology structures exist only for 1D-H and 1D-V type with opposite layout.

On the kinematics of a new parallel mechanism with Schoenflies motion

This paper investigates the kinematics of one new isoconstrained parallel manipulator with Schoenflies motion. This new manipulator has four degrees of freedom and two identical limbs, each having the topology of Cylindrical–Revolute–Prismatic–Helical (C–R–P–H). The kinematic equations are derived in closed-form using matrix algebra. The Jacobian matrix is then established and the singularities of the robot are investigated. The reachable workspaces and condition number of the manipulator are further studied. From the kinematic analysis, it can be shown that the manipulator is simple not only for its construction but also for its control. It is hoped that the results of the evaluation of the two-limb parallel mechanism can be useful for possible applications in industry where a pick-and-place motion is required.

A serial of novel four degrees of freedom parallel mechanisms with large rotational workspace

In this paper, a class of novel four Degrees of Freedom (DOF) non-overconstrained parallel mechanisms with large rotational workspace is presented based on screw theory. First, the conflict between the number of independent constraints applied on the moving platform and the number of kinematic limbs for 4-DOF non-overconstrained parallel mechanism is identified. To solve this conflict, the platform partition method is introduced, and two secondary platforms are employed in each of the parallel mechanisms. Then, the motion requirements of the secondary platforms are analyzed and all the possible kinematic chains are enumerated. The geometrical assembly conditions of all possible secondary limbs are analyzed and some typical non-overconstrained parallel mechanisms are generated. In each of the parallel mechanisms, a planetary gear train is used to connect both of the secondary platforms. The large rotational workspace of the moving platform is obtained due to the relative motion of the two secondary platforms. Finally, the kinematics analysis of a typical parallel mechanism is conducted.

New Structural Representation and Digital-Analysis Platform for Symmetrical Parallel Mechanisms

Abstract An automatic design platform capable of automatic structural analysis, structural synthesis and the application of parallel mechanisms will be a great aid in the conceptual design of mechanisms, though up to now such a platform has only existed as an idea. The work in this paper constitutes part of such a platform. Based on the screw theory and a new structural representation method proposed here which builds a one-to-one correspondence between the strings of representative characters and the kinematic structures of symmetrical parallel mechanisms (SPMs), this paper develops a fully-automatic approach for mobility (degree-of-freedom) analysis, and further establishes an automatic digital-analysis platform for SPMs. With this platform, users simply have to enter the strings of representative characters, and the kinematic structures of the SPMs will be generated and displayed automatically, and the mobility and its properties will also be analysed and displayed automatically. Typical examples are provided to show the effectiveness of the approach.

Symmetry and invariants of kinematic chains and parallel manipulators

This paper presents applications of group theory tools to simplify the analysis of kinematic chains associated with mechanisms and parallel manipulators. For the purpose of this analysis, a kinematic chain is described by its properties, i.e. degrees-of-control, connectivity and redundancy matrices. In number synthesis, kinematic chains are represented by graphs, and thus the symmetry of a kinematic chain is the same as the symmetry of its graph. We present a formal definition of symmetry in kinematic chains based on the automorphism group of its associated graph. The symmetry group of the graph is associated with the graph symmetry. By using the group structure induced by the symmetry of the kinematic chain, we prove that degrees-of-control, connectivity and redundancy are invariants by the action of the automorphism group of the graph. Consequently, it is shown that it is possible to reduce the size of these matrices and thus reduce the complexity of the kinematic analysis of mechanisms and parallel manipulators in early stages of mechanisms design.

Type synthesis of 4-DOF nonoverconstrained parallel mechanisms based on screw theory

A systematic method is developed for the type synthesis of 4-DOF nonoverconstrained parallel mechanisms with three translations and one rotation inspired by the design of H-4. First, the motion requirements of primary platform and secondary platform of the 4-DOF nonoverconstrained parallel mechanisms are analyzed, and the conflict between the number of actuators and the constraint system for nonoverconstrained parallel mechanism is solved. Then, the research topic of type synthesis of 4-DOF nonoverconstrained parallel mechanisms is transformed into the type synthesis of the secondary platform with three translational DOF linked by two chains. On the basis of the screw and reciprocal theory, all possible secondary limbs with 3-DOF, 4-DOF, and 5-DOF are synthesized, respectively. Finally, the configurations and spatial assembly conditions of all possible secondary limbs are provided and some typical mechanisms are sketched as examples.

Type synthesis of parallel mechanisms having the first class GF sets and one-dimensional rotation

A method is presented for the type synthesis of a class of parallel mechanisms having one-dimensional (1D) rotation based on the theory of Generalized Function sets (GF sets for short), which contain two classes. The type synthesis of parallel mechanisms having the first class GF sets and 1D rotation is investigated. The Law of one-dimensional rotation is given, which lays the theoretical foundation for the intersection operations of GF sets. Then the kinematic limbs with specific characteristics are designed according to the 2D and 3D axis movement theorems. Finally, several synthesized parallel mechanisms have been sketched to show the effectiveness of the proposed methodology.

A symmetric parallel Schönflies-motion manipulator for pick-and-place operations

This paper presents a new symmetric parallel Schönflies-motion generator. The design is an evolution of a previous robot with linear inputs. The complete kinematic analysis of the 4-degree-of-freedom (dof) parallel manipulator is presented. The degrees of freedom are obtained from the Group Theory, the direct and inverse position problems are solved obtaining the manipulator's workspace, and the Jacobian analysis is presented. Then the isotropic configurations of the manipulator are discussed and the local dexterity map within the workspace is produced. Finally, two alternatives of a rotational mechanical device, which will increase the angular end-effector range, are proposed.

Uncoupled actuation of overconstrained 3T-1R hybrid parallel manipulators

Based on the Lie-group-algebraic properties of the displacement set and intrinsic coordinate-free geometry, several novel 4-dof overconstrained hybrid parallel manipulators (HPMs) with uncoupled actuation of three spatial translations and one rotation (3T-1R) are proposed. In these HPMs, three limbs are those of Cartesian translational parallel mechanisms (CTPMs) and the fourth limb includes an Oldham-type constant velocity shaft coupling (CVSC). The Lie subgroup of Schoenflies (X) displacements of the displacement Lie group and its mechanical generators with nine categories of their general architectures are recalled. A comprehensive enumeration of all possible Oldham-type CVSC limbs is derived fromX-motion generators. Their constant velocity (CV) transmissions are verified by group-algebraic approach. Then, combining one CTPM and one CVSC, we synthesize a lot of uncoupled 3T-1R overconstrained HPMs, which are classified into nine distinct classes of general architectures. In addition, all possible architectures with at least one hinged parallelogram or with one cylindrical pair are disclosed too. At last, related non-overconstrained HPMs are attained by the addition of one idle pair in each limb of the previous HPMs.

Analyzing kinematics and solving active/constrained forces of a 4-dof 3SPS+SP parallel manipulator

A novel 3SPS+SP parallel manipulator (PM) with 4-dof is proposed. Its kinematics and statics are analyzed systematically. The analytic formulae for solving the displacement, velocity, acceleration, workspace, active forces and constrained force are derived. The analytic results are verified by using a simulation mechanism of the 3SPS+SP PM.

Structural synthesis of maximally regular T3R2-type parallel robots via theory of linear transformations and evolutionary morphology

The paper presents structural synthesis of maximally regular T3R2-type parallel robotic manipulators (PMs) with five degrees of freedom. The moving platform has three independent translations (T3) and two rotations (R2). A method is proposed for structural synthesis of maximally regular T3R2-type PMs based on the theory of linear transformations and evolutionary morphology. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of maximally regular T3R2-type PMs presented in this paper is the 5×5 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Kinematic analysis of maximally regular parallel robots is trivial and no computation is required for real-time control. This paper presents in a unified approach the structural synthesis of PMs with five degrees of freedom with decoupled and uncoupled motions, along with the maximally regular solutions.