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Knowing how to make a multi-locomotion robot achieve locomotion transition under different terrains is a challenging problem, especially for tensegrity robots with multi-locomotion modes. In this study, a motion planning method for the transition of a multi-locomotion tensegrity robot (hereafter TJUBot) under different terrains is proposed. The robot can achieve four locomotion modes: earthworm-like, inchworm-like, tumbling, and sliding locomotion with only two motors. Kinematic models of the four locomotion modes under five typical terrains, including flat ground, confined space, obstacle, gap, and descending slope, are established using the energy method. Meanwhile, the kinematic characteristics (driving law and initial position) of the robot under these terrains are obtained. On this basis, motion planning for the locomotion transition of TJUBot is conducted, which includes a perception strategy based on three laser sensors and a transition strategy under different terrains. The driving laws of the two motors that can ensure the effective locomotion transition of TJUBot under different terrains are naturally obtained. Finally, experiments are conducted. Results demonstrate that the robot can achieve effective locomotion transition when the motion planning method is used.

Inspired by the morphology of human fingers, this paper proposes an underactuated rigid-soft coupled robotic gripper whose finger is designed as the combination of a rigid skeleton and a soft tissue. Different from the current grippers who have multi-point contact or line contact with the target objects, the proposed robotic gripper enables surface contact and leads to flexible grasping and robust holding. The actuated mechanism, which is the palm of proposed gripper, is optimized for excellent operability based on a mathematical model. Soft material selection and rigid skeleton structure of fingers are then analyzed through a series of dynamic simulations by RecurDyn and Adams. After above design process including topology analysis, actuated mechanism optimization, soft material selection and rigid skeleton analysis, the rigid-soft coupled robotic gripper is fabricated via 3D printing. Finally, the grasping and holding capabilities are validated by experiments testing the stiffness of a single finger and the impact resistance of the gripper. Experimental results show that the proposed rigid-soft coupled robotic gripper can adapt to objects with different properties (shape, size, weight and softness) and hold them steadily. It confirms the feasibility of the design procedure, as well as the compliant and dexterous grasping capabilities of proposed rigid-soft coupled gripper.

Purpose: Computer-assisted high tibial osteotomy (HTO) is a frequently used treatment technique for lower extremity orthopedics, and its small incision and low exposure area are major limitations in tibial registration. This work combines skin surface features and gives a suitable registration algorithm based on Iterative Closest Points (ICP) algorithm to improve registration results. Furthermore, the precision, stability and efficiency of the described method is evaluated. Methods: After the initialization stage, the bone surface and skin surface data are combined to construct registration features. Then, a steepest perturbation search method is performed after the ICP algorithm (SPS-ICP) to obtain the optimal transformation through several iterations. Finally, the registration result is evaluated by establishing ground-truth through manual landmarks. Results: Phantom experiments including simulated human tissue show that the proximal fiducial registration error (FRE) of our method can reach 0.80 ± 0.30 mm (mean ± SD) with an overall rotational error < 1° and translational error < 1.5 mm. Furthermore, it remains stable when the point set is sparse. The average registration time is less than 40 s to ensure the high efficiency of surgical operation. Conclusions: The approach fully describes a well-defined framework without additional imaging acquisition equipment for Computer-assisted HTO. By the experiment on the basis of a phantom with simulated soft tissue, the proposed method enables the accurate and robust registration of the tibia, and its computation time meets the demands of surgery.

Parallel manipulator (PM) embraces more kinematic errors than serial mechanism. The substantial errors in PM usually demand more measurements, which leads to low efficiency and affects the accuracy of identification due to the ill-conditioning problem. Having realized this common problem in the kinematic calibration of PMs, we carried out a finite and instantaneous screw (FIS)-based kinematic calibration on a 6-RUHU PM before application to fracture reduction. R, U, and H denote actuated revolute joint, universal joint, and helical joint, respectively. The error model is built by the error mapping of serial chains in the FIS framework. Instead of devoting to the measurement planning for more precise identification, the identifiability of kinematic errors is thoroughly analyzed. Redundant errors are categorized as the ones within limb and among limbs. A minimal identification model is thus defined and an error conversion method is proposed for compensation. Calibration experiments show that the FIS method has an improved accuracy of the 6-RUHU PM at least one magnitude higher than the precision demand, i.e., mean position and orientation errors 0.0574 mm and $5.1197\,\,{\times }\,\, 10^{-4}$ rad after calibration. Compared with the conventional closed-loop vector (CLV) equation method, the accuracy improvement of FIS method is higher. In addition, comparisons with the commonly used configuration selection methods indicate that our method allows random and a smaller number of measurements and can reach satisfactory accuracy.

In this paper, a novel Selective Compliance Assembly Robot Arm (SCARA) high-speed parallel manipulator that can realize three-translation and one-rotation motion is proposed, and an accurate dynamic modeling methodology is investigated. The mechanism is composed of four limbs with a double parallelogram structure and a single moving platform. The high bearing capacity and high dynamic response of the novel mechanism make it a viable alternative choice for this kind of automation equipment. The degree-of-freedom (DOF) of the mechanism is analyzed by the screw theory. At the same time, the velocity mapping model of the mechanism is established by the twist screw and the actuated Jacobian matrix. Then, the acceleration mapping model of the mechanism, including the generalized kinematic pairs, is established by reduced acceleration state, the modified Lie screw, and the acceleration Hessian matrix. On this basis, the complete dynamic model with a compact form of the mechanism is deduced by the combination of screw theory and virtual work principle, and the correctness of the developed model is verified by multibody simulation software. Finally, considering the inertial characteristics of the mechanism, the dynamic performance distribution in the reachable workspace of the mechanism is analyzed by the Joint-Reflected Inertia (JRI) index and Coefficient of Variation of joint-space Inertia (CVI) index, and some areas are selected as the task workspace using the above index to guarantee good dynamic performance.

Purpose: This study intends to evaluate the effectiveness and reliability of defining lower limb alignment based on body surface points. Furthermore, the correlation between measurement error and bone morphology is also evaluated. Methods: A body surface points based method for identifying lower limb alignment is proposed by three steps: Firstly, the CT images of 16 patients (32 legs) are obtained from the hospital CT database. In this manner, the reference anatomical points and the body surface points are measured. Secondly, transformation between body surface points and the equivalent joint centers are defined. Then the lower limb alignment is constructed. Finally, the statistical analysis is carried out to evaluate the error and stability. Results: The coronal alignment can be accurately defined by the body surface points. The deviation caused by central positioning of the knee joint of the femur is 0.385 ± 0.306° (range: 0.004–1.519; 95% CI 0.279–0.492), and the error is not correlated with bone length (R = -0.015), bone width (R = 0.105), and bone length-to-width ratio(R = -0.080); the deviation due to central positioning of the tibial knee joint is 0.658 ± 0.509° (range: 0.040–1.815; 95% CI 0.482–0.835), and the error is independent of bone length (R = − 0.110), bone width (R = − 0.150), and bone length-to-width ratio(R = 0.117); the deviation due to central positioning of the ankle joint is 0.387 ± 0.301° (range: 0.007–0.963°; 95% CI 0.283–0.492), and the error is not correlated with bone length (R = − 0.062), bone width (R = 0.047), and bone length-to-width ratio(R = − 0.105). Conclusions: The method of defining equivalent joint center based on body surface points is applicable to different anatomical positioning. The identification of lower limb alignment is noninvasive and has high accuracy, especially for coronal alignment. However, it has limitations in the sagittal view. In addition, there is no correlation between the error and bone morphology.

Interior assembling inside the cabin of an aircraft requires assembling robot to be light-weight and able to carry heavy payload. This paper proposed a hybrid robot and carried out its optimal design and experiments. The robot consists of a 1T2R parallel module and a 2T serial module. In the parallel module, the first limb is composed of a slider crank mechanism and a RS link. The other two limbs are PRS limbs. Herein, R, S, P are revolute, spherical, and actuated prismatic joints. Optimization of the robot concerns motion/force transmissibility, total mass, and stiffness. Hence, kinematic, stiffness, and mass modeling are implemented, and then the Pareto-based multi-objective optimization. Objective arrangements are discussed by concerning (1) the conflicting relation between mass and the minimal linear stiffness along z-axis and (2) the overall stiffness performance. After comparing six multi-objective optimizations, it is found that simultaneously regarding mass and minimal linear stiffness along z-axis as objectives is beneficial for obtaining large payload-to-mass ratio, moreover having overall stiffness as objectives would lower the values of motion/force transmissibility and payload-to-mass ratio. Finally, optimization model having motion/force transmissibility, total mass, and minimal linear stiffness along z-axis as objectives is selected. The optimal payload-to-mass ratio is up to 13.2837. The five degrees-of-freedom hybrid robot is machined and assembled. Experiments on the workspace, repeatability, and load carrying capacity confirm the performances of the designed robot.

The application of 3D visualization technology in building construction has also increased. The study used Revit software to construct a 3D building information model (BIM) for the exhibition space of Chuzhou Higher Education City Development Collaborative Innovation Center to achieve a 3D visualization display; based on the 3D visualization, a particle swarm optimization (PSO) algorithm was used to find the optimal path for the exhibition space, so as to achieve the layout design of the exhibition space. The PSO algorithm was optimized in terms of inertia weight, acceleration coefficient, and initial population to obtain the improved PSO (IPSO) algorithm. The experimental results showed that the optimal path found by the IPSO algorithm was 78.56 meters in distance, 98.2 seconds in time consumption, and 50.11% in smoothness, which were better than the other two algorithms. Meanwhile, the IPSO algorithm had a lower value of particle fitness function, indicating that the IPSO algorithm had the highest performance and the strongest path finding ability among the three algorithms. It is confirmed that it is feasible to use the IPSO algorithm for optimal visit path finding in 3D environment. It is effective to visualize the exhibition space in 3D by constructing a BIM.

This paper deals with geometric error modeling and sensitivity analysis of an over-constrained parallel tracking mechanism. The main contribution is the consideration of over-constrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore, two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.

Currently, accumulating documents have paid great attention to the critical role of long non-coding RNAs. The long non-coding RNAs DLEU1 has been demonstrated to be dysregulated in many solid tumors and hematological malignancies. However, the detailed descriptions about its potential roles and molecular mechanism in gastric cancer (GC) are still blurry. As for our research, it was found out that DLEU1 was observably intensified in GC tissues and cell lines. And highly expressed DLEU1 was relevant to tumor size, advanced stage of pathology and lymph node metastasis in GC patients. Silenced DLEU1 obviously suppressed proliferation via leading to the cell cycle arrest and inducing cell apoptosis of GC. Furthermore, mechanistic experiments uncovered that DLEU1 could recruit LSD1 (lysine specific demethylase 1) to the promoter regions of KLF2 and then suppressed its transcription. In addition, rescue assays revealed that the oncogenic function mediated by DLEU1 in GC was partly by regulating KLF2. Collectively, our findings manifested that DLEU1 might serve as an oncogene in GC.

In order to meet the requirements of large downward force and high stiffness performance for the friction stir welding process, this paper proposes a 5 degree-of-freedom hybrid manipulator as friction stir welding robot. It is composed of a 3 degree-of-freedom redundant parallel module and a 2 degree-of-freedom rotating head. Semi-analytical stiffness model of the hybrid manipulator is firstly established by compliance models of the two substructures. Virtual work principle, deformation superposition principle and twist/wrench mapping model are applied to this compliance modeling process. A novel instantaneous stiffness performance index is then proposed on the basis of instantaneous energy defined by reciprocal product of external payload screw and corresponding deformation screw. It solves the problems of inconsistent physical unit of linear/angular stiffness and is able to evaluate overall and worst-case stiffness performance. Next, stiffness/compliance experiments are carried out to verify the stiffness model and the novel instantaneous stiffness performance index. Finally, stiffness performance of 5 degree-of-freedom hybrid manipulator is thoroughly discussed in terms of engineering requirements, worst-case stiffness performance and stiffness singularities. It can be summarized that the semi-analytical stiffness model and the novel instantaneous stiffness index are effective in analyzing and evaluating stiffness performance of the 5 degree-of-freedom hybrid manipulator.

Determining the motions and constraints of serial kinematic chains in a concise and visual way is an inevitable step in the analysis and design of both serial and parallel mechanisms. The now most used method is the numerical approach which resorts to solving linear equations. By introducing Clifford algebra, this paper intends to propose an analytical approach to determine the unknown 6-n(n< 6) constraints (motions) from the known nmotions (constraints) of serial kinematic chains in different configurations only by drawing some auxiliary points, lines, and planes. The axes and action lines of motions and constraints are characterized by the lines that would be described by Clifford algebra. These lines can be determined analytically according to the relations among points, lines, and planes, which have been expressed by using the operation rules of Clifford algebra Cl(0, 3, 1) such as inner, outer, dual, and shuffle products. Based upon the mechanics principle that the constraint does not work on the motion, the unknown 6-nconstraints (motions) of serial kinematic chains from known nmotions (constraints) are determined both in an analytical algebraic form and in a visual manner. Finally, four examples are given to demonstrate how to use this approach and test its validity. The merit of this approach is beneficial to the digital analysis and design of both the serial and parallel mechanisms by means of computer and programming languages.

Coalburst is one of the most serious disasters that threaten the safe production of coal mines, and this disaster is particularly serious in China. This paper presents an overview of coalbursts in China since 1980s. From the "stress and energy" and "regional and local" perspectives, the achievements in the theory, practice and management of coalbursts in China are systematically summarized. A theoretical system of coalbursts has been formed to reveal the deformational behavior of coalbursts and explain the mechanism of coalbursts. The occurrence conditions of coalbursts are put forward and the critical stress is obtained. The stress index method for risk evaluation of coalbursts before mining is proposed, and the deformation localization prediction method of coalbursts is put forward. The relationship between energy release and absorption in the process of coalbursts is found, and the prevention and control methods of coalbursts, including the regional method, the local method and support, are presented. The safety evaluation index of coalburst prevention and control is put forward. The integrated prevention and control method for coal and gas outbursts is proposed. The prevention and control technology and equipment of coalbursts have also been developed. Amongst them, the distribution law of the critical stress in China coalburst mines is discovered. The technology and equipment for monitoring, prevention and control of coalbursts, as well as for integrated prevention and control of combined coalbursts and other disasters, have been developed. The energy-absorbing and coalburst-preventing support technology for roadways is invented, and key engineering parameters of coalburst prevention and control are pointed out. In China, coalburst prevention and control laws and standards have been developed. Technical standards for coalbursts are formulated, statute and regulations for coal mines are established, and regulatory documents are promoted.

This paper focuses on the type synthesis of two degree-of-freedom (2-DoF) rotational parallel mechanisms (RPMs) that would be applied as mechanisms actuating the inter-satellite link antenna. Based upon Lie group theory, two steps are necessary to synthesize 2-DoF RPMs except describing the continuous desired motions of the moving platform. They are respectively generation of required open-loop limbs between the fixed base and the moving platform and definition of assembly principles for these limbs. Firstly, all available displacement subgroups or submanifolds are obtained readily according to that the continuous motion of the moving platform is the intersection of those of all open-loop limbs. These subgroups or submanifolds are used to generate all the topology structures of limbs. By describing the characteristics of the displacement subgroups and submanifolds intuitively through employing simple geometrical symbols, their intersection and union operations can be carried out easily. Based on this, the assembly principles of two types are defined to synthesize all 2-DoF RPMs using obtained limbs. Finally, two novel categories of 2-DoF RPMs are provided by introducing a circular track and an articulated rotating platform, respectively. This work can lay the foundations for analysis and optimal design of 2-DoF RPMs that actuate the inter-satellite link antenna.

Multi-scale casting parts are important components of high-end equipment used in the aerospace, automobile manufacturing, shipbuilding, and other industries. Residual features such as parting lines and pouring risers that inevitably appear during the casting process are random in size, morphology, and distribution. The traditional manual processing method has disadvantages such as low efficiency, high labor intensity, and harsh working environment. Existing machine tool and serial robot grinding/cutting equipment do not easily achieve high-quality and high-efficiency removal of residual features due to poor dexterity and low stiffness, respectively. To address these problems, a five-degree-of-freedom (5-DoF) hybrid grinding/cutting robot with high dexterity and high stiffness is proposed. Based on it, three types of grinding/cutting equipment combined with offline programming, master-slave control, and other technologies are developed to remove the residual features of small, medium, and large casting parts. Finally, the advantages of teleoperation processing and other solutions are elaborated, and the difficulties and challenges are discussed. This paper reviews the grinding/cutting technology and equipment of casting parts and provides a reference for the research on the processing of multi-scale casting parts.

Driven by the requirements of the bionic joint or tracking equipment for the spherical parallel manipulators (SPMs) with three rotational degrees-of-freedom (DoFs), this paper carries out the topology synthesis of a class of three-legged SPMs employing Lie group theory. In order to achieve the intersection of the displacement subgroups, the subgroup characteristics and operation principles are defined in this paper. Mainly drawing on the Lie group theory, the topology synthesis procedure of three-legged SPMs including four stages and two functional blocks is proposed, in which the assembly principles of three legs are defined. By introducing the circular track, a novel class of three-legged SPMs is synthesized, which is the important complement to the existing SPMs. Finally, four typical examples are given to demonstrate the finite displacements of the synthesized three-legged SPMs.

In order to study the failure process of an anchorage structure and the evolution law of the body’s deformation field, anchor push-out tests were carried out based on digital speckle correlation methods (DSCM). The stress distribution of the anchorage interface was investigated using the particle flow numerical simulation method. The results indicate that there are three stages in the deformation and failure process of an anchorage structure: elastic bonding stage, a de-bonding stage and a failure stage. The stress distribution in the interface controls the stability of the structure. In the elastic bonding stage, the shear stress peak point of the interface is close to the loading end, and the displacement field gradually develops into a “V” shape. In the de-bonding stage, there is a shear stress plateau in the center of the anchorage section, and shear strain localization begins to form in the deformation field. In the failure stage, the bonding of the interface fails rapidly and the shear stress peak point moves to the anchorage free end. The anchorage structure moves integrally along the macro-crack. The de-bonding stage is a research focus in the deformation and failure process of an anchorage structure, and plays an important guiding role in roadway support design and prediction of the stability of the surrounding rock.

Abstract: Existing testing techniques do not meet the requirements for static-dynamic composite loading tests of anti-impact supports for rockburst protection in mines. In this study, a hydraulic impact test machine was designed to simulate the rockburst conditions. The test machine was designed with the maximum impact load of 6500 kN, starting time (for static-dynamic loading conversion) of less than 50 ms, effective impact displacement of 0.8 m, maximum impact speed of 8 m/s, and a maximum energy accumulation of 8 × 106J. Based on the proposed technical specifications, a symmetrical layout of four accumulator groups was opted to meet the impact energy requirements. Secondly, a novel extra-high-flow high-pressure quick-opening valve structure (with rated pressure of 31.5 MPa, an instantaneous flow rate of 120,000 L/min, and starting time &lt; 50 ms) was innovatively designed and shown to sufficiently meet the maximum impact speed requirement. Furthermore, an impact cylinder with a blowing device was developed to minimize the liquid return resistance of the hydraulic impact cylinder for achieving the required impact load and speed. An anti-rigid impact protector is also proposed to protect the test machine during high-energy impact tests. The design validation was performed through various tests. The results confirm that the test machine successfully provides a reliable method for laboratory dynamic testing of anti-impact supports. In addition, the data collected during the tests can be used for future development of novel anti-impact hydraulic supports. Article Highlights: Designed a novel static-dynamic composite loading test machine for rockburst in mines. Designed an innovative extra high flow and pressure traffic quick opening valve to re-create rockburst scenario. Developed a new cylinder structure to meet impact load and speed requirement by minimizing liquid return resistance.

Abstract: A study of dimensional synthesis of a 3-DOF parallel manipulator with coupling of translation and rotation is carried out. The architecture of the manipulator is composed of a moving platform attached to a fixed base through three identical PRS (prismatic-revolute-spherical) serial limbs, whose unique topology leads to the physical unit inconsistency of the conventional Jacobian matrix and the emergence of the parasitic motion. Then this paper introduces a kinetostatic performance index of the manipulator based on the condition of a dimensionally homogeneous Jacobian matrix, later, the workspace of the aforementioned manipulator is searched and the influence of the crucial design variables on the workspace is analyzed. Finally, a dimensional synthesis method of the manipulator is proposed, which may be regarded as a nonlinear programming problem with subject to the parasitic motion and other several engineering constraints.

When the rock burst occurs, energy absorption support is an important method to solve the impact failure. To achieve constant resistance performance of energy absorption device, as an important component of the support, the mechanical properties of one kind of prefolded tube is analyzed by quasi-static compression test. The deformation process of compression test is simulated by ABAQUS and plastic strain nephogram of the numerical model are studied. It is found that the main factors affecting the fluctuation of force-displacement curve is the stiffness of concave side wall. The original tube is improved to constant resistance by changing the side wall. The friction coefficient affects the folding order and form of the energy absorbing device. Lifting the concave side wall stiffness can improve the overall stiffness of energy absorption device and slow down the falling section of force-displacement curve. It is always squeezed by adjacent convex side wall in the process of folding, with large plastic deformation. Compared with the original one, the improved prefolded tube designed in this paper can keep the maximum bearing capacity (Pmax), increase the total energy absorption (E), improve the specific energy absorption (SEA), and decrease the variance (S2) of force-displacement curve.

Topology and performance are the two main topics dealt in the development of robotic mechanisms. However, it is still a challenge to connect them by integrating the modeling and design process of both parts in a unified frame. As the properties associated with topology and performance, finite motion and instantaneous motion of the robot play key roles in the procedure. On the purpose of providing a fundamental preparation for integrated modeling and design, this paper carries out a review on the existing unified mathematic frameworks for motion description and computation, involving matrix Lie group and Lie algebra, dual quaternion and pure dual quaternion, finite screw and instantaneous screw. Besides the application in robotics, the review of the work from these mathematicians concentrates on the description, composition and intersection operations of the finite and instantaneous motions, especially on the exponential-differential maps which connect the two sides. Furthermore, an in-depth discussion is worked out by investigating the algebraical relationship among these methods and their further progress in integrated robotic development. The presented review offers insightful investigation to the motion description and computation, and therefore would help designers to choose appropriate mathematical tool in the integrated design and modeling and design of mechanisms and robots.

Object recognition is a prerequisite to control a soft gripper successfully grasping an unknown object. Visual and tactile recognitions are two commonly used methods in a grasping system. Visual recognition is limited if the size and weight of the objects are involved, whereas the efficiency of tactile recognition is a problem. A visual–tactile recognition method is proposed to overcome the disadvantages of both methods in this article. The design and fabrication of the soft gripper considering the visual and tactile sensors are implemented, where the Kinect v2 is adopted for visual information, bending and pressure sensors are embedded to the soft fingers for tactile information. The proposed method is divided into three steps: initial recognition by vision, detail recognition by touch, and a data fusion decision making. Experiments show that the visual–tactile recognition has the best results. The average recognition accuracy of the daily objects by the proposed method is also the highest. The feasibility of the visual–tactile recognition is verified.

Multi-objective optimization of a typical parallel tracking mechanism considering parameter uncertainty is carried out in this paper. Both dimensional and sectional parameters are regarded as design variables. Workspace, kinematic, stiffness, and dynamic performances are simultaneously considered in formulating optimal objectives and constraint conditions. Considering manufacturing and assembling errors, parameter uncertainty is modeled and evaluated to minimize their effects on the optimized performances. Analytical models between objectives and design variables are established to improve the efficiency of optimization while its accuracy is assured. The study of parameter uncertainty and analytical mapping model is incorporated in the optimization of the parallel tracking mechanism. With the aid of particle swarm algorithm, a cluster of solutions, called Pareto frontier, are obtained. By proposing an index, a cooperative equilibrium point representing the balance among objectives is selected and the optimized parameters are determined. The present study is expected to help designers build optimized parallel tracking mechanism in an effective and efficient manner.

Parallel tracking mechanism with varied axes has great potential in actuating antenna to track moving targets. Due to varied rotational axes, its finite motions have not been modeled algebraically. This makes its type synthesis remain a great challenge. Considering these issues, this paper proposes a conformal geometric algebra (CGA) based approach to model its finite motions in an algebraic manner and parametrically generate topological structures of available open-loop limbs. Finite motions of rigid body, articulated joints, and open-loop limbs are formulated by outer product of CGA. Then, finite motions of parallel tracking mechanism with varied axes are modeled algebraically by two independent rotations and four dependent motions with the assistance of kinematic analysis. Afterward, available four degrees-of-freedom (4-DoF) open-loop limbs are generated by using revolute joints to realize dependent motions, and available five degrees-of-freedom (5-DoF) open-loop limbs are obtained by adding one finite rotation to the generated open-loop limbs. Finally, assembly principles in terms of minimal number and combinations of available open-loop limbs are defined. Typical topological structures are synthesized and illustrated.

A novel 5-axis hybrid reconfigurable robot named Tricept-IV, including one 4-degree-of-freedom (4DOF) hybrid module and one 2DOF end effector, is investigated. Compared with extensive research that has been pursued for the parallel kinematic machines such as Tricept, Sprint Z3 Head, and so on, the hybrid kinematic machines have not adequately been studied. This paper demonstrates a method of workspace decomposition applied in the dimensional synthesis of a 4DOF hybrid module, which is the underlying architecture of the newly invented robot. This paper starts with an introduction of the Tricept-IV robot. After dividing the 4DOF hybrid module into one position-orientation coupling (POC) subsystem and one position-feed (PF) subsystem, its workspace is decomposed into POC and PF subspaces accordingly, and then the inverse position problem may be solved by means of one prejudgment method. Furthermore, the Jacobian matrix of the POC subsystem is obtained by the screw theory so as to formulate its kinematic performance index. Finally, the dimensional synthesis based on workspace decomposition of the hybrid module is carried out by taking a global view of the dimensional synthesis of these two subsystems.