The research of a biomimetic robotic manipulator is based on the flexible characteristics of the human upper limb joint, and a biomimetic robotic elbow joint plays a very significant role in the kinematic control of the biomimetic robotic manipulator. Most robotic elbow joints encountered today have a common disadvantage of bad neutrality, low rotational capability, and poor biomimetics. To overcome some difficulties, this paper presents a novel biomimetic robotic elbow joint. The structural model of the elbow joint is described, and the position equation is solved. Secondly, the kinematic equation of the elbow joint is established, the kinematic decoupling performance evaluation index of the elbow joint is defined, the kinematic decoupling characteristics of the elbow joint are analyzed, and the kinematic decoupling performance map in the workspace is drawn. Thirdly, using the spatial model theory, the structural parameters of the elbow joint are optimized, the structural parameters are selected by the Monte Carlo method, and the novel biomimetic robotic elbow joint is designed. The analysis results showing the kinematic decoupling performance of the elbow joint are symmetrical and the kinematic decoupling performance decreases with the increase of the angle, and there is a good kinematic decoupling in the workspace of about 35% in the vicinity of the initial position. When the structural parameters of the elbow joint are
Biomimetic robotics is a new branch in the field of robot researches, which have integrated the biomimetic principle into the design and control of the robot and could imitate structure and movement characteristics of animals or humans. The motion behavior and some functions of natural organism have provided a great deal of thinking sources for robot scientists to design and realize flexible control [
The research of a biomimetic robotic manipulator is based on the flexible characteristics of the human upper limb joint and dexterous hands, and the human upper limbs are composed of the shoulder joint, elbow joint, wrist joint, and finger joint to complete the complex work and reflect the flexibility of the whole limb movement. The more flexible the upper limb joint, the more flexible the upper limb movement can be controlled [
Cui and Jin [
The problem of decoupling is closely related to the Jacobian matrix of the biomimetic robotic joint. Researchers have studied less in this field. Gong et al. [
Based on the analysis of the literature, the existing robotic elbow joint is usually able to achieve flexion and extension. The structure of elbow joint design adopts a series structure; the series structure lacks good centering ability. From the analysis of the performance of elbow joints, there are many literatures on the bearing capacity of elbow joints, and the literature of the kinematic decoupling has not been seen yet. On this basis, this paper proposes a biomimetic robotic elbow joint. The biomimetic robotic elbow joint adopts a 2-DOF spherical parallel mechanism as a prototype which has advantages of good structural characteristics, large range of motion, and high bearing capacity and was compared with the 3-DOF parallel mechanism in the 863 project. From the analysis of the degree of freedom of the mechanism, the 3-DOF spherical parallel mechanism has three degrees of freedom in accordance with the requirements of the prosthetic prototype of the shoulder joint, and the human elbow joint structure has two degrees of freedom of movement characteristics, so the elbow joint mechanism has very good bionic structure. From the analysis of the installation of the mechanism, the rotation center of the 3-DOF spherical parallel mechanism is located in the middle of the moving platform and the static platform. The neutrality requirements for the rods during installation are very high and difficult to install. The rotation center of each rod of the biomimetic robotic elbow joint presents 90 degrees, which is convenient to install and has good neutrality.
In this paper, the kinematic equation of the biomimetic robotic elbow joint is established, the Jacobian matrix is derived, the kinematic decoupling performance evaluation index of the biomimetic robotic elbow joint is defined, the kinematic decoupling performance evaluation index map is drawn in the workspace, and the global kinematic decoupling performance index is established based on the kinematic decoupling analysis. Based on the space model theory, the structural parameters of the elbow joint are optimized and selected by the Monte Carlo method, and the biomimetic robotic elbow joint is designed. The purpose of the decoupling analysis of the elbow joint is to make the control of the elbow joint mechanism more convenient and easier.
The biomimetic robotic elbow joint is an important joint of the biomimetic hand. On the base of the knowledge of bionics, the human elbow joint is composed of the humerus, radius, ulna, and ligament. The human elbow joint is limited to the connection between the three bones and the ligament, which can only rotate about two axes and can realize movement of internal rotation and external rotation and flexion and extension, as shown in Figure
Schematic diagram of the human elbow joint.
The structure design of the biomimetic robotic elbow joint should be able to realize the movement of the anthropomorphic elbow joint. According to the analysis of joint structure and kinematic characteristics of the human elbow joint, this paper proposed a novel biomimetic robotic elbow joint based on a 2-DOF orthogonal spherical parallel mechanism. The elbow joint has two moving branches, the frame and the moving platform, which contain two driving motors, and the driving motor is fixed on the frame. The moving platform of the elbow joint is connected by the arm connector and connected with the ring through the rotating pair. The elbow joint can realize two degrees of freedom of rotation and has advantages of good bionic characteristics, small structure, and little inertial forces. The structure diagram is shown in Figure
The structure of the biomimetic robotic elbow joint. 1—frame, 2 and 3—connecting rods, 4—annular member, 5—moving platform, and 6—arm connector.
Two Cartesian coordinates, the base frame
Assume that the spherical radius of the reference center of the connection rotation pairs
The kinematic equation of the elbow joint is established based on the solution of the inverse position. The attitude angles of the elbow joint moving platform are
In the fixed coordinate system, the unit vector
According to the mechanism characteristics of the elbow joint, the input angle of the drive motor is
Comparison of (
In the fixed coordinate system, the unit vector
In the fixed coordinate system, the unit vector
According to the geometry of the elbow joint, (
Equations (
The inverse position solution equation of the elbow joint can be written as
The forward positive solution equation of the elbow joint by (
Differential treatment (
The kinematic decoupling analysis of the elbow joint depends on the Jacobian matrix
The decoupling analysis of the kinematic of the elbow joint is to study the correlation or dependence of the output parameters on the input parameters. If the Jacobian matrix When the input angular velocity of the The elbow joint has an input angular velocity on the From ( When the input angular velocities of the When the elbow joint is driven by two driving motors, ( In Figure
Index of the kinematic decoupling performance of output angle velocity when the input velocity has the
The global performance index can better reflect the kinematic decoupling of the elbow joint in the whole posture workspace, and the spatial model theory [
Based on the structural description of the biomimetic robotic elbow joint, the structural parameters are
The dimensionless structural dimensions of the elbow joint are expressed, respectively, as
Formula (
Considering the manufacturing and assembling of the biomimetic robotic elbow joint, the conditions for the structural parameters are satisfied and can be written as
The three dimensionless structure parameters are Cartesian axes
The spatial model of the biomimetic robotic elbow joint.
Three-dimensional model of the spatial model
Two-dimensional model of the spatial model
The global performance index is introduced into the spatial model, and the global kinematic decoupling performance index of the biomimetic robotic elbow joint is defined as
Using MATLAB software, the global kinematic decoupling performance map of the elbow joint in the plain geometric space model is drawn according to (
Globe kinematic decoupling performance evaluation index atlases of the elbow joint.
From Figure
Structural parameters have a direct influence on the kinematic performance of the robot. Stan et al. [
The value range of the global kinematic decoupling performance index of the elbow joint is the interval [0, 1], which conforms to the rule of rectangle distribution. Combined with the structural features of the elbow joint, the structural parameter ranges of the elbow joint
In [
Under the condition that the evaluation index of the global kinematic decoupling performance is better than the optimization target value, the distribution rule of sampling values of each parameter counted the sampling within the range of structural parameters, and the probability distribution of the structural parameters is obtained, as shown in Figure
Probability distribution of the discrete histogram for the structure parameters for the biomimetic robotic elbow joint.
The probability of
The probability of
The probability of
Considering its processing and assembling process, the virtual prototype of the elbow joint is designed based on the optimized structure parameters, and primary technical parameters are shown in Table
The primary technical parameters of the biomimetic robotic elbow joint.
Design parameter | Technical index |
---|---|
Degree of freedom | 2 |
Flexion | 45° |
Extension | 45° |
Internal rotation | 50° |
External rotation | 45° |
90 mm | |
70 mm | |
30 mm | |
Motor | Maxon 273755 |
Coupling | Maxon 326665 |
Encoder | MR TL 256-1024 CPT |
The virtual prototype model of the biomimetic robotic elbow joint is shown in Figure
A novel biomimetic robotic elbow joint virtual prototype. 1, 3, 9, 11, 16, 18, 19, 20, 25, 26, and 27—revolute joints; 2 and 10—short bars; 4—frame; 5—upper arm; 6—long bar; 7 and 13—motor; 8 and 14—connectors; 12–15—motor bases; 17 and 23—connecting rods; 21—annular member; 22—moving platform; and 24—arm connector.
Servo motor 13 is installed on motor base 15, and servo motor 13 transmits the torque of the motor to carrier rod 23 through the planar four-bar mechanism. The other movement branch of the biomimetic robotic elbow joint is servo motor 7 mounted on elbow base 5. Servo motor 7 is fixedly connected with the rotating shaft on the bottom of connecting rod 17 through the mounting hole of coupling 8. Connecting rod 17 is connected to annular member 21 by a pair of coaxial rotating hinges 18 and 19. The other pair of coaxial rotary hinges 26 and 27 on annular member 21 is connected to moving platform 22. Arm connector 24 is fixedly connected to the bottom of the moving platform.
In order to verify the correctness of the kinematic equations of the elbow joint mechanism, the results of the theoretical solution of the elbow joint and the simulation of the kinematic model are compared and analyzed. The movement trajectory of the biomimetic robotic elbow joint moving platform is expressed by
According to (
The input angle velocity curve of the elbow joint.
A virtual prototype of the biomimetic robotic elbow joint is established, and a virtual simulation experiment is performed. Based on the Core software, the elbow joint is parametric designed. The parameter design range is the same as the parameter range in the spatial model theory. The parametric design variable increment is 5 mm, and 343 virtual prototypes of elbow joints with different structural dimensions were obtained.
The kinematic simulation of the reachable workspace is carried out for each prototype, and the total volume number of workspaces and the number volume of workspaces conforming to the kinematic decoupling index are recorded.
The structural parameters were obtained by optimizing the spatial model, which are 30 mm, 70 mm, and 90 mm. The kinematic decoupling workspace volume number is taken as the standard value
The 343 elbow joint movement decoupling volume numbers are compared with the basic kinematic decoupling volume number. When one structural parameter is changed and the other parameters are unchanged in the standard prototype, the volume number of kinematic decoupling workspaces is acquired, and the influence curve of each structural parameter on the size of the elbow joint kinematic decoupling workspace is drawn, as shown in Figure
The influence curve of structural parameters on the kinematic decoupling workspace volume ratio.
In Figure
The kinematic decoupling analysis of a novel biomimetic robotic elbow joint was performed. Analysis of the kinematic decoupling of the elbow joint is symmetrical in the workspace, and the motion is completely decoupling when driven by a single motor. The global kinematic decoupling performance of the elbow joint showed a linear distribution. With the increase of
In summary, the biomimetic robotic elbow joint has two degrees of freedom and good decoupling characteristics, which can be applied in rehabilitation robot, biomimetic robot, industrial robot, humanoid robot arm, and other fields.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by the Chinese National Natural Science Fund (E51505124), Hebei Provincial Natural Science Foundation (E2017209252), Department of Education of Hebei Province (QN2015203 and 2015GJJG084), and Online Education Research Fund of Education Research Center of the Ministry of Education (2016YB117).