Underactuated robotics: A review <s> UR wrist <s> From the Publisher: ::: The first book devoted to robot wrists, this text/reference describes the various morphologies of wrist actuators through the lavish use of photographs, and diagrammatic and isometric drawings. Displays the most significant robot wrists of the past, now is use, and under development. Provides background material covering history of robot wrists, and use of the human wrist as a model for robot wrist actuators. All types of wrist actuators are surveyed, and new wrist designs are disclosed in full detail. Treatment is practical--there are helpful design guidelines, with specific design techniques and methods. Also includes a detailed, annotated bibliography of patents, articles, and books. <s> BIB001 </s> Underactuated robotics: A review <s> UR wrist <s> This paper presents the first and second order kinematic analysis of a three-degrees-of-freedom 3-RPS parallel robot mechanism. The position and orientation parameters of the moving platform of this mechanism are six, however only three of them are independent. The Jacobian of the mechanism is a 3 by 6 rectangular matrix. This imposes difficulties on the kinematic analysis of this mechanism. This paper presents a method to formulate three motion constrain equations which are consistent with the kinematic structure of the mechanism, and establishes the velocity and acceleration relationship between the independent output motions and three input parameters in close form. <s> BIB002 </s> Underactuated robotics: A review <s> UR wrist <s> This paper presents the formulation of the inverse kinematics and dynamics of the 3-RRS parallel platform with three degrees of freedom. For inverse kinematics, the position analysis is first performed. Then the differential motion constraint equations of the movable platform are established, based on which the velocity and acceleration formulae of leg actuators are derived. In the inverse dynamic analysis, the parallel platform is decomposed into two parts through parting the three spherical joints, and the forces acting on the parted joints are determined according to the moment (and force) equilibrium's of the legs and the movable platform. Subsequently, the analytic expressions of the driving moments of the leg actuators are derived by means of the moment equilibrium of the legs. Although only the 3-RRS parallel platform is analyzed, the presented method and process can also be applied to other less DOF parallel platforms. <s> BIB003 </s> Underactuated robotics: A review <s> UR wrist <s> In this paper, we study the singularity loci of a special class of spherical three-degree-of-freedom parallel manipulators. The concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the direct and inverse kinematic solutions of these manipulators, respectively. As mentioned elsewhere, there are three different types of singularities for parallel manipulators, each having a different physical interpretation. These types are considered and it is shown that, for the manipulators considered here, the three types of singularities coincide. Moreover, for the two types of manipulators studied here, there are only four singular configurations in the Cartesian space. In addition, the three-dimensional graphical representations of the singularity loci in the joint and in the Cartesian spaces are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control. <s> BIB004 </s> Underactuated robotics: A review <s> UR wrist <s> In this paper we present a novel pointing parallel mechanism with fully decoupled degrees of freedom. The mechanism consists of two interconnected slider-crank linkages, each one of which independently actuates one of the Euler angles of the output link. Motors can be mounted on the frame. The parallel architecture provides the mechanism with compactness and robustness, while decoupling of motion guarantees a wide workspace, an easy mathematical treatment, and a simple control. Such a mechanism may be suitable for applications that require aiming bodies such as tools, telescopes, antennas, cameras, solar panels, human or humanoid artificial limbs, particularly if requisites on dimensions and stoutness on the one hand and mobility on the other are stringent. <s> BIB005 </s> Underactuated robotics: A review <s> UR wrist <s> This paper presents a methodology for the analytical determination and representation of the workspace boundaries of symmetrical spherical parallel mechanisms (SPMs). The methodology is based on an intuitive orientation representation which, while not well known, has proven to be very useful for the analysis of symmetrical parallel mechanisms. The latter, previously introduced as "tilt-and-torsion angles," are briefly described. Then, relatively simple analytical expressions are found for the workspace boundaries of general symmetrical SPMs. Next, using these expressions and a simple numerical procedure, a fast algorithm is proposed for representing the so-called constant-torsion workspace. Finally, several examples are provided <s> BIB006 </s> Underactuated robotics: A review <s> UR wrist <s> Recursive matrix relations for kinematics and dynamics of the 3-RRR Agile Wrist spherical parallel robot are established in this paper. The prototype of the robot is a three-degrees-of-freedom mechanism with three identical legs. Controlled by concurrent torques, which are generated by some electric motors, the active elements of the robot have three independent rotations. Knowing the rotation motion of the moving platform, we develop first the inverse kinematical problem and determine the velocities and accelerations. Further, the principle of virtual work is used in the inverse dynamic problem. Matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model. <s> BIB007 </s> Underactuated robotics: A review <s> UR wrist <s> In this paper we address the forward kinematics problem of a parallel manipulator and propose an iterative neural network strategy for its real-time solution to a desired level of accuracy. Parallel manipulators are closed kinematic structures that possess requisite rigidity to yield a high payload to self-weight ratio. Because of this unique feature, they have been employed in manufacturing, flight simulation systems, and medical robotics. However, it is this closed kinematic structure that has led to difficulty in their kinematic control, especially the forward kinematics control. The iterative neural network strategy we propose employs a trained neural network and an error compensation algorithm in the feedback loop. The proposed strategy was tested with data from a real-world flight simulation system. Results show that solutions with a maximum error in the position and orientation parameters of 0.25 mm and 0.01°, respectively, can be achieved in less than five iterations (or about 1 second). Because of the nature of this strategy, it is possible to implement it in a hardware form, which can result in a multi-fold reduction in the solution time for the same accuracy level. <s> BIB008 </s> Underactuated robotics: A review <s> UR wrist <s> This paper is an attempt to design a decoupled A/B-axis tool head with parallel kinematics, due to the increasing demand for A/B-axis tool heads in industry, particularly in thin wall machining applications for structural aluminium aerospace components. In order to carry out further analysis, the method of orientation description based on the azimuth and tilt angles is introduced, which is a convenient method describing kinematics, parasitic motions, and orientation workspace. For the purpose of optimal design, three indices are defined to evaluate the force transmission performance of the tool head. They have obvious physical significance and are dependent of any coordinate system. Based on the indices and their performance atlases, the optimization process is presented in detail. The parasitic motions and orientation capability of the designed tool head are analyzed finally. The results show that the designed device is far from singularity, has good force transmissibility, and has very high tilting angl... <s> BIB009 </s> Underactuated robotics: A review <s> UR wrist <s> The passive motion of the knee, i.e. the motion in virtually unloaded condition, is efficiently modelled by means of a parallel spherical wrist. Compared to previously presented models, it results in a much simpler solution, with a lower number of members and kinematic pairs. The model is used to replicate the passive motion of an experimentally analysed knee. Finally, the accuracy of this new model is compared to that of a more complex one, previously presented in the literature, which already proved to be effective. <s> BIB010 </s> Underactuated robotics: A review <s> UR wrist <s> This paper deals with the design of a new class of hybrid mechanism dedicated to humanoid robotics application. Since the designing and control of humanoid robots are still open questions, we propose the use of a new class of mechanisms in order to face several challenges that are mainly the compactness and the high power to mass ratio. Human ankle and wrist joints can be considered more compact with the highest power capacity and the lowest weight. The very important role played by these joints during locomotion or manipulation tasks makes their design and control essential to achieve a robust full size humanoid robot. The analysis of all existing humanoid robots shows that classical solutions (serial or parallel) leading to bulky and heavy structures are usually used. To face these drawbacks and get a slender humanoid robot, a novel three degrees of freedom hybrid mechanism achieved with serial and parallel substructures with a minimal number of moving parts is proposed. This hybrid mechanism that is able to achieve pitch, yaw, and roll movements can be actuated either hydraulically or electrically. For the parallel submechanism, the power transmission is achieved, thanks to cables, which allow the alignment of actuators along the shin or the forearm main axes. Hence> the proposed solution fulfills the requirements induced by both geometrical, power transmission, and biomechanics (range of motion) constraints. All stages including kinematic modeling, mechanical design, and experimentation using the HYDROiD humanoid robot's ankle mechanism are given in order to demonstrate the novelty and the efficiency of the proposed solution. <s> BIB011 </s> Underactuated robotics: A review <s> UR wrist <s> The majority of the manipulation tasks require the motion of the end-effector from an initial pose to a final one without any particular condition on the path. Thus, the reduction of the practicable paths between any two poses is a possible choice, exploitable at the design stage, for simplifying the manipulator hardware. This choice is adopted in underactuated manipulators. The (nS)-2SP U wrist is one out of the underactuated parallel wrists this author proposed in a previous paper. Here, the kinematic analysis of this wrist is studied: both its finite and its elementary kinematics are considered. It is shown that its control algorithms can be written by using simple closed-form formulas, which can take advantage from the wide literature on the spherical four-bar linkages. Moreover, the demonstration that its singular configurations can be avoided more easily than the ones of the fully parallel wrist is provided. <s> BIB012 </s> Underactuated robotics: A review <s> UR wrist <s> The functional synthesis of mechanisms is involved in the problem solving process to finding functional chains of mechanisms in conceptual design, which has an essential effect on the product innovation. However, existing approaches for functional synthesis of mechanisms are either inextensible to achieve functional chains of complex mechanisms or prone to a loss of optimal solutions under the consideration of mechanical efficiency and cost. This paper is devoted to a systematic dynamic programming-based methodology for constrained functional synthesis of mechanisms with the consideration of mechanical efficiency and cost. After a general functional representation model based on the motional element pair is proposed, an exhaustive dynamic programming functional synthesis algorithm of two motional elements pair is then proposed to produce functional chain solutions with consideration of mechanical efficiency and cost. The functional synthesis of new devices for jacking up system of an offshore platform is given as an example, which demonstrates that the methodology is obviously helpful to produce valuable functional chains of mechanism solutions with consideration of mechanical efficiency and cost. <s> BIB013 </s> Underactuated robotics: A review <s> UR wrist <s> Conceptual design of mechanisms is an early stage in the product design process, which has an essential effect on product innovation. However, existing approaches for automated synthesis of mechanisms are either inextensible to achieve the conceptual design of complex mechanisms or prone to a loss of optimal solutions with consideration of mechanical efficiency. This paper is devoted to a systematic weighted directed graph-based methodology for automated synthesis algorithm of mechanisms under mechanical efficiency consideration. After the motion element pair is proposed, a general functional representation model is then put forward to generate a motion functional graph. An exhaustive functional synthesis of motion element pair with K-highest mechanical efficiency algorithm is then proposed to produce solutions with K-highest mechanical efficiency. To curb the combinatorial explosion and evaluate optimal combinatorial solutions effectively, design constraint verification approach and design evaluation app... <s> BIB014 </s> Underactuated robotics: A review <s> UR wrist <s> The workspace denotes the work area of a robot, which is an important foundation of designing a robot. As formulating the suitable workspace models for a robot wrist is very crucial for analyzing its behavior, many researches have been focused on it in recent decades with a result of many valuable contributions. However, current researches always focus on rigid and full actuated robot wrist, while the robot wrist is always a multibody system, which can affect the accuracy of workspace analysis and simulation. This paper proposed a model of workspace analysis of a novel underactuated robot wrist based on virtual prototyping. After the conceptual design of a novel underactuated mechanism was introduced, the degree of freedom of the underactuated robot wrist was calculated. Then the detailed design of underactuated robot wrist was done. The whole workspace model of the robot system was then established. It was indicated that the working points in the workspace of the robot were distributed compactly and uniformly, which can meet design requirements with high efficiency. The workspace analysis of underactuated robot wrist and the accuracy analysis of underactuated robot wrist were also put forward. The result was testified by the simulation on Matlab, which demonstrated that the methodology is obviously helpful for robot design. <s> BIB015 </s> Underactuated robotics: A review <s> UR wrist <s> Dynamics of robot wrist is concerned with the relations between the forces acting on the robot wrist mechanism and the accelerations it produces. Many valuable contributions come forth in recent years, as a suitable dynamics model for a robot wrist is very crucial for analysing its behaviour, on-line control of motions and forces, trajectory design and optimization, and design of robot mechanisms. However, current researches always focus on full-actuated robot wrists. The proposed underactuated robot wrist is a novel mechanism with fewer actuators than the degrees of freedom. As the existing dynamics models for the full-actuated robot wrists are not suitable for the underactuated robot wrist anymore, the dynamics model of the underactuated robot wrist becomes an important issue. This article is devoted to a model for dynamics analysis of a novel underactuated robot wrist. After this underactuated robot wrist is introduced, the dynamics analysis of the underactuated robot wrist with numerical simulation ba... <s> BIB016 </s> Underactuated robotics: A review <s> UR wrist <s> As an underactuated mechanism, the accuracy analysis of the spherical 3 degrees of freedom (3-DOF) parallel underactuated robot wrist becomes an important issue. However, current researches in the accuracy analysis always focus on the full-actuated mechanism. In this paper, the loop incremental method is applied to the accuracy analysis of the spherical 3-DOF parallel underactuated robot wrist. After the novel underactuated robot wrist is introduced, this paper presents the loop selection rules. According to the above rules, four loops are selected from the underactuated robot wrist. After error model of each loop is proposed, the error model of the underactuated robot wrist, including both position error and orientation error, is then established by the loop incremental method. After the accuracy analysis of the underactuated robot wrist is verified with the experiments on coordinate measuring machine, the robot wrist is then guided to be assembled with the minimum global error. The result is testified to demonstrate that the methodology is helpful for robot design. <s> BIB017 </s> Underactuated robotics: A review <s> UR wrist <s> Functional synthesis of mechanisms plays a crucial role in mechanical product design, which has an essential effect on the product innovation and cost. However, current functional synthesis algorithms of mechanisms are either inextensible to achieve complex mechanism solutions or prone to a loss of optimal solutions without consideration of cost. This article proposed a systematic kinematic state-based methodology for functional synthesis of mechanisms under cost consideration. After a general functional representation model based on the kinematic state pair is proposed with a result of the kinematic state space, an exhaustive functional synthesis of the kinematic state pair with the lowest cost algorithm is then proposed to produce solutions with K-lowest cost. The functional synthesis of a feeding mechanism device for cold heading machine is given as an example, which demonstrates that the methodology is obviously helpful to produce valuable functional chain solutions with low cost. <s> BIB018 </s> Underactuated robotics: A review <s> UR wrist <s> The synthesis of mechanisms has an important effect in the product development. A mechanism has two basic kinds of functions, i.e. to transform motion and to transform force. However, current methods always focus on either motion synthesis or force synthesis. The paper proposed a dynamic programming-based synthesis of multi-input or multi-output mechanisms with the simultaneous consideration of motion and force transmission. A general function model is proposed with a result of function matrix of mechanisms. After the solving process of single input and single output (SISO) system using dynamic programming algorithm is proposed, the single input and multiple outputs (SIMO) system, and the multiple inputs and single output system (MISO) are also discussed in detail, together with design evaluation. The synthesis of mechanisms for jacking up system in offshore platform is taken as an example, which demonstrates that the methodology is helpful to produce valuable mechanisms. <s> BIB019 </s> Underactuated robotics: A review <s> UR wrist <s> As concerning the present gap in the dynamic information association and integration between engineering design and engineering analysis, this paper is devoted to a parametric skeleton model-based dynamic information association and integration between design model and analysis model. After the description of the gap between engineering design and analysis was analysed, the modeling method of the product skeleton model was proposed. Then the integrated design and analysis method based on the skeleton model was proposed based on the parameterized design method for analysis. The parametric skeleton model-based design modeling method could be used to resolve the integrating design and analysis problem in product design. The integrated design and analysis of an offshore crane were given as an example with about 25 % time reduction in design cycle, which demonstrates that the methodology is helpful to the associativity of design-analysis models. <s> BIB020 </s> Underactuated robotics: A review <s> UR wrist <s> Dynamics of robot wrist is concerned with the relations between the forces acting on the robot wrist mechanism and the accelerations it produces. Many valuable contributions come forth in recent years, as a suitable dynamics model for a robot wrist is very crucial for analysing its behaviour, on-line control of motions and forces, trajectory design and optimization, and design of robot mechanisms. However, current researches always focus on full-actuated robot wrists. The proposed underactuated robot wrist is a novel mechanism with fewer actuators than the degrees of freedom. As the existing dynamics models for the full-actuated robot wrists are not suitable for the underactuated robot wrist anymore, the dynamics model of the underactuated robot wrist becomes an important issue. This article is devoted to a model for dynamics analysis of a novel underactuated robot wrist. After this underactuated robot wrist is introduced, the dynamics analysis of the underactuated robot wrist with numerical simulation based on virtual prototyping is proposed in detail. The peak values of servo motor in the joint motion unit are also estimated. The dynamics analysis of a novel underactuated robot wrist is used to demonstrate the proposed method. <s> BIB021 </s> Underactuated robotics: A review <s> UR wrist <s> ABSTRACTConceptual design has essential impacts on the carbon footprint of a product. Existing product models for conceptual design always focus on knowledge modelling and knowledge organisation, etc. However, the traditional approach is lack of better comprehending representation and reuse of low-carbon design knowledge for low-carbon conceptual design. This paper is devoted to presenting a feature-based integrated modelling approach of product model for low-carbon conceptual design to make the knowledge of functional design be transferred efficiently to the principle conceptual design and structure conceptual design, and even subsequent design process. The feature-based integrated representation model with carbon footprint information about function, effect and structure concept are put forward step by step, and then an integrated principle solution model for low-carbon conceptual design is presented based on the generalised assembly model. The knowledge representation and organisation method of princip... <s> BIB022 </s> Underactuated robotics: A review <s> UR wrist <s> Abstract Space robotics is taken as one of the most promising approaches for on-orbit servicing missions. The underactuated non-holonomic parallel mechanism is a new direction of parallel space robotics, with small volume, lightweight, low cost, low energy consumption, and high flexibility. The existing methods on type synthesis could not generate underactuated non-holonomic parallel mechanisms with the introduction of the non-holonomic spherical pairs in parallel mechanisms. This paper is devoted to type synthesis of underactuated parallel mechanisms with spherical motion pattern accompanied by the generation of the non-holonomic spherical pairs in parallel mechanisms with spherical motion pattern. After the introduction of the traditional roller-sphere contact, this paper proposes a novel roller-sphere contact. After this paper provides the type synthesis of parallel mechanisms with spherical motion pattern, it puts forward the generation method of non-holonomic spherical pairs in parallel underactuated mechanisms with spherical motion pattern. The non-holonomic underactuated joint mechanism of a space robot for on-orbit servicing operations is taken as an example to demonstrate the proposed method. <s> BIB023 </s> Underactuated robotics: A review <s> UR wrist <s> Abstract The sustainable product design is one of the most effective approaches to achieve cleaner production with special consideration for environmental impacts of products, as the cleaner production is a recent global concern for manufacturing. At the early stage of sustainable design, it is a challenge to understand each individual customer's requirements, and achieve the transformation from these sustainable functional requirements to the design parameters. This paper is devoted to an approach to achieve the mapping from the functional domain to the physical domain, and transforming fuzzy sustainable functional requirements into design parameters, mainly according to the multi-level requirement information description of the products. After the general model of sustainable functional requirements is proposed, the model of fuzzy sustainable functional requirements is discussed in detail. It introduces a computational approach to achieve the mapping from sustainable functional requirements to design parameters during the mapping process from the functional domain to the physical domain. The exoskeleton robot is used to demonstrate the proposed methodology. <s> BIB024 </s> Underactuated robotics: A review <s> UR wrist <s> Abstract The majority of product environmental footprints for a product are determined at the design stage of its life cycle, especially in conceptual design. However, it is difficult to achieve the solution evaluation for product environmental footprint with unascertained product information in conceptual design. This paper is devoted to conceptual design evaluation for product environmental footprint using unascertained measure model. After the unascertained measure model based on the Unascertained Mathematical Theory is introduced, the evaluation process of solutions in conceptual design for product environmental footprint based on unascertained measure model is discussed in detail. And the product conceptual design for product environmental footprint integrated with unascertained measure model-based evaluation approach is also proposed. The conceptual design of the offshore wind power installation platform is given as an example, which demonstrates that the methodology is helpful to design evaluation in conceptual design for product environmental footprint. <s> BIB025 </s> Underactuated robotics: A review <s> UR wrist <s> Abstract Product carbon footprint has a profound impact on the sustainable manufacturing. Due to the uncertainty of product information, it is a crucial issue to estimate product carbon footprint for product life cycle. The paper is devoted to the product carbon footprint estimation model based on the unascertained mathematics theory. After the introduction of unascertained mathematics theory, the integration of the estimation data through unascertained number is discussed in detail. After the model of product carbon footprint for product life cycle is proposed, the estimation method of carbon footprint in the product life cycle based on the unascertained number model is discussed in detail. The product carbon footprint of a modular underactuated exoskeleton robot mechanism is given as an example to demonstrate the proposed methodology. <s> BIB026 </s> Underactuated robotics: A review <s> UR wrist <s> Abstract As the product environmental footprint (PEF) has a profound impact on the environmental sustainability, it is crucial to estimate PEF in the product life cycle. The existing researches lack the prescriptiveness and environmental footprint-specific accounting guidance to produce consistent PEF, thus most of the existing PEF models fail for product life cycle. The paper is devoted to PEF assessment for product life cycle. After the introduction of PEF, the calculation model for each of the 14 kinds of PEF is proposed. PEF assessment process is then put forward in detail, which includes 10 steps, i.e. functional unit selection, system boundary determination, impact types selection, data collection, impact types classification, impact types characterization, impact types of PEF calculation, impact types standardization, impact types grouping and weighting, PEF assessment result. PEF assessment process of an agricultural picking robot is used to demonstrate the effectiveness of the proposed methodology. <s> BIB027 </s> Underactuated robotics: A review <s> UR wrist <s> Abstract The product sustainability assessment is a progress to evaluate sustainability with indicators for product sustainability in the whole product life cycle. However, the current approaches could not deal with the relationships of those closed-loop indicators. This paper is devoted to a graph theory-based product sustainability assessment approach to avoid those closed loops of the evaluation indicators. The hierarchical evaluation system for mechanical product sustainability assessment with energy, environmental, resource, technical, and economic indicators is proposed. The product sustainability assessment approach is proposed with five steps: rationalization of the directed graph of the evaluation system, construction of the hierarchical structure, transformation from reachability matrix to judgment matrix, consistency check and adjustment of judgment matrix, and indicator weight determination and comprehensive assessment of evaluation system. The product sustainability assessment of an underactuated exoskeleton robot is given as an example to demonstrate the proposed methodology. <s> BIB028
Current research has focused on rigid and fully powered robotic wrists, which are always a multi-body system that affects the accuracy of workspace analysis and simulation. For the synthesis of the mechanical structure of multi-body systems, He and Huang BIB018 presented a new systematic kinematic state-based methodology for the functional synthesis of mechanisms with consideration of cost. He and Hua BIB019 presented a new systematic dynamic programming-based methodology for the synthesis of mechanisms integrated with force and motion transformation. He et al. BIB013 presented a new systematic dynamic programming-based methodology for functional synthesis of mechanisms with the considerations of mechanical efficiency and cost. He et al. BIB014 were devoted to a systematic weighted directed graph-based methodology for automated synthesis algorithm of mechanisms under mechanical efficiency consideration. For modeling of prototypes or products, He et al. BIB020  are working on a new computational coevolutionary product design approach. An undirected graph of the mechanical parameters is proposed to simulate the relationship between the design parameters. Parametric design methods are used to solve design and analysis problems. After he proposed the first UR wrist in the world, He et al. BIB015 proposed a workspace analysis model for a new UR wrist based on virtual prototyping. The numerical simulation analysis of the wrist dynamics of UR based on virtual prototype is introduced in detail. The peak value of the servo motor in the articulation unit was also estimated. BIB021 The inverse kinematics analysis and forward kinematic analysis of the UR wrist with numerical simulation based on virtual prototyping were discussed in detail. BIB016 He et al. BIB017 proposed a loop selection rule and applied the loop increment method to the accuracy analysis of a spherical three-DOF parallel UR wrist. Combined with the particularity of the spherical wrist structure and the versatility of the D-H parameters, Wang et al.  proposed a fast and accurate parameter identification method for wrist calibration. Prof. He has important research and contributions in . 3-RRS parallel mechanism for underactuated parallel joint. BIB023 International Journal of Advanced Robotic Systems the field of three-DOF parallel robot wrists. He et al.     invented several new three-DOF UR wrist devices based on ball hinges and spherical spaces. The utility model has the advantages of simple structure, low cost, lightweight, small volume, easy processing, and easy maintenance. It could be used as a robotic arm or a robot arm with multiple series mechanisms. On this basis, He et al.   BIB027 designed and invented the novel UR wrist based on the centering mechanism and non-holonomic constraints, which has the characteristics of flexible movement, compact structure, and good rigidity. It could be used as the joint of the robot. The novel UR wrist could be used in parallel robots, micromotion robots, and the like. The robot wrist BIB001  BIB007 BIB004 BIB002 was used to connect the robot arm and the end effector, so that the end effector could achieve a certain gesture in the working position. Therefore, the wrist of the robot could be described as the positioning mechanism of the robot. The robot wrist is an important and complex structure of the robot, whose flexibility directly determines the type and complexity of tasks that a robot could accomplish. Therefore, it is necessary to research the robot wrist. BIB011 Robots need six DOFs to achieve any position and attitude in the working position, and their wrists should have three DOFs. The robot wrist could be either serial or parallel mechanism. BIB008 BIB009 BIB006 The wrist of the serial robot is composed of the kinematic chain of RRR mechanism (R stands for the rotating pair). Structure diagram and threedimensional (3-D) model of three-DOF UR wrist are shown in Figures 10 and 11 . In Figures 10 and 11 , the wrist of a parallel robot is composed of multiple kinematic chains, which could accomplish tasks more accurately than that of a serial wrist. BIB007 BIB012 Actuators of parallel robot wrists could be easily isolated from the operating space by placing it on a fixed base. The parallel robot wrist has a high stiffness configuration in almost all of its workspace and a reduced working space. There are two basic types of robot wrist mechanisms. Serial mechanism. Three DOFs could be achieved by using an open-loop kinematic chain, while requiring three power sources to move. Sometimes, it is also reduced to two DOFs. The loss of DOF could be compensated by other DOF from the robot arm.  Most continuous wrists in robot have three rotating joints. Chablat and Angeles 100 proposed a universal n-revolute spherical robot wrist and studied the existence of redundant isotropic structures in the wrists of four rotating series of spherical robots. Parallel mechanism. The movement of the wrist of the three-DOF parallel robot resembles the real wrist with different characteristics. BIB010 BIB005 BIB003 The simple feature is the 3-RRR mechanism, which has three rotating joints per leg. The structure of the parallel mechanism is relatively simple compared to the structure of the bionic mechanism. The spatial layout is more compact than the series mechanism. Compared with the single motion mechanism, it is more compact than the actual wrist movement. Therefore, it has advantages in the design and selection of robot wrist. Meanwhile, underactuated parallel mechanism is used to reduce the number of drivers and the costs of control and hardware with the development underactuated researches. This article presents a new underactuated parallel robot wrist with 3-RRR characteristics. The current underactuated mechanism research has three main characteristics: 1. Mechanism innovations are mainly concentrated on underactuated fingers, while UR arms and wrists are rarely innovative. 2. At present, the research of underactuated mechanism is still in the plane state. Space underactuated mechanism is one of the study directions in the future. 3. The reachable workspace and mechanism tolerance of the underactuated mechanism is one of the main study directions. The mechanism of the UR, from concept design to prototype or product, should be designed based on the low carbon concept for sustainable product design. BIB022 Sustainable product design is one of the most effective ways to achieve cleaner production, especially considering the environmental impact of the product. Because cleaner production is a recent concern for global manufacturing. BIB024 The environmental footprint of most products is determined during the design phase of their life cycle, especially in conceptual design. However, it is difficult to achieve a solution assessment of the product's environmental footprint by unconfirmed product information in conceptual design. BIB025 He et al. BIB026 are working on a product carbon footprint estimation model based on unascertained mathematical theory. The product carbon footprint of the modular underactuated exoskeleton robotic mechanism is given as an example to illustrate the proposed method. He et al. BIB025 used the unascertained measurement model to evaluate the conceptual design of the product environmental footprint. Taking the conceptual design of the offshore wind power installation platform as an example, the method is helpful for the design evaluation of the product environmental footprint conceptual design. After the design of the electromechanical concept of the UR mechanism is completed, a product sustainability assessment is required. Product sustainability assessments are progress in assessing sustainability, including indicators of product sustainability throughout the product life cycle. He et al. BIB028 proposed a grading evaluation system for the sustainability assessment of mechanical products using energy, environmental, resource, technical, and economic indicators. The product carbon footprint of the modular underactuated exoskeleton robot mechanism is used to demonstrate the proposed method.