TWI568942B - Spherical coordinates orientating parallel mechanism - Google Patents

Description

Ball coordinate steering parallel mechanism

The invention relates to a ball coordinate steering parallel mechanism, which can complement the deficiencies of the traditional balance ring (Gimbals) mechanism, and provides a bearing mechanism for various torsion output devices, telescopic lifting mechanisms and observation positioning devices for spherical latitude and longitude movement.

The current mechanism commonly used for spherical latitude and longitude movement is the traditional balanced gimbal mechanism. It is allowed to carry various torque output devices, telescopic lifting mechanisms and observation positioning devices to rotate at a large angle or even continuously. But this organization is a ring-by-loop architecture. The load must be placed in the inner ring, the motor and the gearbox are connected to the inner ring to drive the bearing to rotate the latitude axis, so the motor and gear box of the outer ring must load the inertia of the motor and the gear box with the inner ring to drive the outer ring. The ring rotates against the longitude axis. If the bearing volume or inertia is large, the inner and outer ring radii must also be augmented, making it difficult to approximate the bulk of the operating space. Moreover, the balanced ring mechanism is also associated with problems such as telecommunication transmission and harness winding due to the ring-by-loop architecture.

The brief description of the present invention is that the double tetrahedral structure end line is coaxially connected to the four-group inner rail arc and the outer rail arc ball ball coordinate steering mechanism. A perspective view of the combined configuration of the present invention is shown in Fig. 1 , and a front view and a side view are shown in Fig. 2 . The invention can be further divided into an external type and a built-in type.

The invention comprises: an outer frame structure (4o) four end corners respectively bonding four sets of outer rail arc rods (2o), and four sets of inner rail arc rods (1o) and outer rail arc rods (2o) are axially connected to each other, It is used to convey the output of the outer frame rotating device (4a) to the inner frame structure (3o) and the terminal bearing (3d).

The top end of the outer frame structure (4o) is respectively connected to the outer frame rotating device (4a), and then respectively connected to the outer end of the outer rail arc bar (2o), and the outer frame rotating device (4a) can be a torque output device. Or the angle detector, the outer frame structure (4o) can be fixed by the outer frame bracket (4b), as shown in Fig. 3 .

The outer shaft (2o) is connected to the outer core (2a) and the outer frame rotating device (4a) is connected to the shaft. The outer rail (2o) and the inner rail (1o) are connected to the shaft. (2b) Shaft connection, the inner end of the inner rail arc rod (1o) is connected to the inner frame structure (3o) by the inner shaft core (1a), as shown in Fig. 4 .

The inner frame structure (3o) is used to receive the torque output from the four sets of inner rail arc (1o) and outer rail arc (2o) groups. The four inner rail arc rods (1o) are respectively axially connected to the four end corners of the inner frame structure (3o). The outer frame of the inner frame structure (3o) is connected to the inner frame rotating device (3a) to drive the terminal arc bar (3c) to meet the timely displacement requirement of the ball coordinate steering. If there is no timely displacement requirement, the inner frame can be rotated. The device (3a) directly fixes the terminal arc bar (3c) at one end corner of the inner frame structure (3o). The inner frame rotating device (3a) may be an angle detecting device (3b), such as an optical encoder, for measuring the relative angular change between the inner rail arcing rod (1o) and the inner frame structure (3o) for precision verification. Ball coordinate steering angle; if the torque output inner frame rotation device (3a) is required to be a torque output device, it will increase the system design complexity; finally, the terminal load (3d) is fixed outside the terminal arc bar (3c). End, as shown in Figure 5 .

The ball coordinate steering parallel mechanism of the invention can be divided into an external type and a built-in type. The external terminal bearing (3d) is applied to the shoulder or hip joint of the robot, or the torque output device is mounted, such as the clamping module of the machine tool, as shown in Fig. 5 . If the external terminal bearing (3d) is mounted as a telescopic lifting mechanism with a variable arm, such as a pneumatic cylinder, a hydraulic cylinder or an electric screw cylinder, the inner frame bracket (3e) is designed to assemble the heavy plate to balance the weight. Reduce torque variation, as shown in Figure 7 . If the built-in terminal carrying (3d) is a measuring device with a large volume or inertia, such as a laser, a telescope, etc., the design terminal arc (3c) is placed inside the inner frame structure (3o), as shown in Fig. 8. .

(1)‧‧‧Internal rail arc group

(1o) ‧‧‧ inner rail arc

(1a)‧‧‧Inner shaft core

(2) ‧‧‧ outer rail arc group

(2o) ‧‧‧ outer rail arc

(2a)‧‧‧External shaft core

(2b) ‧‧‧Connected shaft core

(3) ‧‧‧Internal frame structure and terminal bearer

(3o) ‧‧‧ inner frame structure

(3a)‧‧‧Inner frame turning device

(3b)‧‧‧ Angle detector

(3c) ‧‧‧terminal arc

(3d) ‧ ‧ terminal bearer

(3e)‧‧‧Inner frame bracket

(4) ‧‧‧Outer frame structure and frame rotating device

(4o) ‧‧‧ frame structure

(4a)‧‧‧Outer frame turning device

(4b)‧‧‧Front bracket

Figure 1 Stereo view of ball coordinate steering parallel mechanism assembly configuration

Figure 2: Ball coordinate steering parallel mechanism assembly configuration front view and side view

Figure 3 is a three-dimensional view and geometric definition of the outer frame structure and the outer frame rotating device

Figure 4 : Stereo view and geometric definition of four sets of inner rail and outer rail arcs

Figure 5 internal frame structure and terminal bearer stereo view and geometric definition

Figure 6: The inner frame bracket and the counterweight plate are fitted with a flat telescopic lifting mechanism.

Figure 7 shows the built-in design of the device based on the large amount of inertia

Figure 8 is designed to match the geometric definition of the frame

Fig. 9a Interference phenomenon of any two arc rod interaction

Figure 9b Singular phenomenon of biaxial docking of right angle arc

Figure 10a is a singular phenomenon with the four-axis collinearity of the long arc

Figure 10b Singular phenomenon of four-axis collinearity of long and short arcs

The geometric definition, key problems and solutions of the various components of the ball coordinate steering mechanism of the present invention are described below.

A. Geometry definition:

The geometry of the outer frame structure (4o) is defined as a tetrahedron, and the core wires of the four sets of torsion output devices must coincide with the angular line of the outer frame tetrahedron. The body of the outer frame tetrahedron is marked as o _u , and the corner line of the outer frame tetrahedron is indicated as the unit vector u _i ( i =1~4), and the angle between the corner lines of each corner is marked as Λ _ij ( i , j =1~ 4; i ≠ j ), expressed in vector inner product: Λ _ij = cos ^-1 [ u _i . u _j ], as shown in Figure 3 . If the outer frame structure (4o) is a regular tetrahedron, the angle between the six corners of each corner is equal to about 109.5°, ie: Λ ₁₂ = Λ ₁₃ = Λ ₁₄ = Λ ₂₃ = Λ ₂₄ = Λ ₃₄ 109.5°. If the outer frame structure (4o) is a regular tetrahedron, it is easier to design and simulate the parameters because of its single symmetry. However, it must be noted that the regular tetrahedron must have the singularity of the four-axis collinearity, as described later. Therefore, the outer frame design must conform to the tetrahedral geometry definition without having to be a regular tetrahedron, and its shape can also be designed as shown in Fig. 6 .

The geometric definition of four sets of inner rail arc rods (1o) and outer rail arc rods (2o): the four outer rail arc rods (2o) have equal radii, and the four inner rail arc rods (1o) have equal radii. The four sets of inner rail arc rods (1o) and outer rail arc rods (2o) must be concentric with each end shaft, that is, four sets of external shaft cores (2a), medium joint shaft cores (2b) and inner joint shaft cores ( 1a) It can change with the attitude of the inner frame structure (3o), but the axis must point to the body center of the outer frame tetrahedron. The unit vector of the i-th external core (2a) is denoted as u _i , the unit vector of the i-th core (2b) is denoted as w _i , and the unit vector of the i-th inner core (1a) is denoted as v _i . The radius of the four outer rail arcs (2o) is denoted by r _u , and the radius of the four inner rail arcs (1o) is denoted by r _v . The arc length of the i-th outer rail arc (2o) is denoted by α _i and is defined as the angle between the ith outer shaft core (2a) and the ith intermediate shaft core (2b), which can be expressed by the vector inner product: α _i = cos ^-1 [ u _i . w _i ]. The arc length of the i-th inner rail arc (1o) is denoted by β _i and is defined as the angle between the ith inner core (1a) and the ith intermediate core (2b), which can be expressed by the vector inner product: β _i = Cos ^-1 [ v _i . w _i ], as shown in Figure 4 . In order to avoid the singular phenomenon: the arc lengths of the four sets of outer rail arcs (2o) do not have to be equal, and the arc lengths of the four inner rail arcs (1o) do not have to be equal, as will be described later. The geometry of the inner frame structure (3o) is defined as a tetrahedron, so that the four end angles of the inner frame tetrahedron are equal to the body center, and the axis of the inner frame rotating device (3a) must coincide with the angular line of the inner frame tetrahedron. , as shown in Figure 5 . The body of the inner frame tetrahedron is marked as o _v , the angle of the inner frame tetrahedron is indicated as the unit vector v _i ( i =1~4), and the angle between the inner corners of the inner frame structure (3o) is indicated as Ω _ij ( i , j =1~4; i ≠ j ), which can be expressed in vector inner product, ie: Ω _ij = cos ^-1 [ v _i . v _j ], as shown in Figure 5 . If the inner frame structure (3o) is just a regular tetrahedron, the angle between the corners of each corner is equal to about 109.5°, ie: Ω ₁₂ = Ω ₁₃ = Ω ₁₄ = Ω ₂₃ = Ω ₂₄ = Ω ₃₄ If the inner frame structure of 109.5° is a regular tetrahedron, it is easier to design and simulate the parameters because of its single symmetry. However, it must be noted that the regular tetrahedron must have the singularity of the four-axis collinearity, as described later. Therefore, the inner frame structure (3o) design must conform to the tetrahedral geometry definition without having to be a regular tetrahedron, and its shape can also be designed as shown in Fig. 7 and Fig. 8 .

2. The key to the problem

The key to the problem of the invention is how to control the four sets of outer rail arcs (2o) or inner rails (1o) that are not in line with each other and operate smoothly? That is how to avoid the occurrence of so-called interference and singularity? The following describes the unique interference and the uniqueness of the present invention. The singular phenomenon is used as a reference for parameter design.

(1) Interference phenomenon: This so-called interference refers to the phenomenon that the operation path of one arc pole is blocked by another arc rod. Let the sum of the arc lengths of the two outer rail arcs (2o) be equal to the angle between the corners of the corresponding two outer frames, ie: α _i + α _j = Λ _ij ( i , j =1~4; i ≠ j ) The mutual interference of the two outer rail arcs (2o) during operation can be completely avoided, as shown in Fig. 9a . Similarly, the sum of the arc lengths of any two inner rail arcs (1o) is equal to the angle between the corners of their respective two inner frames, ie: β _i + β _j = Ω _ij , which can completely avoid any two inner rail arcs (1o) interactive interference. However, when the sum of the arc lengths of any two outer rail arcs (2o) or inner rail arcs (1o) is the smallest, the movement space is also relatively limited to almost no.

It can be seen from the above that the sum of the arc lengths of any two outer rail arcs (2o) must be greater than the angle between the two corners of the corresponding outer frame, namely: α _i + α _j Λ _ij , if the outer frame tetrahedron is a regular tetrahedron, the sum of the arc lengths of any two outer rail arcs (2o) must be greater than 109.5°; the sum of the arc lengths of any two inner rail arcs (1o) must be greater than its corresponding The angle between the inner corners of the inner frame, namely: β _i + β _j Ω _ij , if the inner frame tetrahedron is a regular tetrahedron, the sum of the arc lengths of any two inner rail arcs must be greater than 109.5°. According to the geometry of the mechanism, the sum of the arc length of any inner rail and its outer rail arc cannot be greater than 180° or lose meaning, ie: α _i + β _i 180° ( i =1~4). If the physical structure is not included, it can be assumed that when the sum of the arc lengths of the four inner rails (1o) and the outer rails (2o) is equal to 180°, the range of rotation of the payload compartment is the largest, but In fact, it is impossible to disregard structural entities. At this time, the probability of interaction interference is the largest, and the motion space is the smallest, as shown in Figure 9b . It can be seen that the sum of the arc length of any inner rail (1o) and outer rail (2o) must be less than or equal to 180°, ie: α _i + β _i 180°.

It can be known that the steering space cannot be restricted by avoiding interference, and the path of the evasive path can be selected according to the trajectory of the desired trajectory. There is no absolute optimal parameter design value.

(2) Singularity: This so-called singularity means that the torsional output of any torsion output device cannot be completely transmitted to the end angle of its corresponding inner frame, so that it can be correspondingly moved. The singular phenomenon known in the present invention can be roughly divided into Single-axis collinear singularity, dual-axis docking singularity and four-axis collinear singularity. The uniaxial collinear singularity is that the inner i -arc (1o) of the i-th group is equal to the arc length of the outer-arc (2o), ie: α _i = β _i ( i =1~4), which occurs in the inner frame When the i- th angle line coincides with the i-th angle line of the outer frame, that is, u _i = v _i . Single-axis collinear singularity is not enough, because if only a single torque output device is not available for delivery, there are other torque output devices available to operate to control the desired steering.

The two-axis docking singularity is a phenomenon in which the two-torque output device cannot be completely transmitted with the output. The premise is that the sum of the arc lengths of the inner rails (1o) and the outer rails (2o) of both groups is equal to 180°, ie: α _i + β _i = α _j + β _j = 180° ( i , j =1~4; i ≠ j ). Occurs within the first frame i, j and the angle of the center line of the frame i, j when the angle of the center line of abutment, _{namely: u i = - v i;} u j = - v j. At this time, no matter how the two torque output devices rotate, the two end angles of the inner frame connected thereto cannot be correspondingly moved, and the other two-axis torque output devices can be operated but not enough to control the set ball coordinate steering angle. To avoid this phenomenon, fortunately, the premise of the parameter design is not established, namely: α _i + β _i ≠ 180 °. Then, with the above intersection, it is obtained that the sum of the arc lengths of any inner rail and its outer rail arc must be less than 180°, that is, α _i + β _i <180°.

The most difficult to avoid is the four-axis collinear singularity, the premise is that the four sets of inner rail arcs (1o) and the outer rail arcs (2o) are equal in length, namely: α ₁ = β ₁ ; α ₂ = β ₂ ; α ₃ = β ₃ ; α ₄ = β ₄ , occurs when the four corners of the inner frame coincide with the four corners of the outer frame, ie: u ₁ = v ₁ ; u ₂ = v ₂ ; u ₃ = v ₃ ; u ₄ = v ₄ , as shown in Figure 10a . At this time, the four sets of torque output devices can not actuate the four end angles of the inner frame regardless of the rotation. Since the four-axis collinear singularity occurs at the pole of the ball coordinate, once it is difficult to detach from the misplacement, the pole is often the initial or the point of reduction, so it is difficult to avoid.

Third, the solution

Method 1: According to the previous example, the premise of the parameter design is not established, that is, the four sets of inner rail arc rods (1o) and outer rail arc rods (2o) arc lengths are not equal to each other. The greater the difference between the inner rail arc rod (1o) and the outer rail arc rod (2o) arc length, the torque output of each group when the four inner rail arc rods (1o) and the outer rail arc rod (2o) are completely collinear. The larger the effective arm of the device can be controlled, the easier it is to get out of trouble, as shown in Figure 10b . However, the problem is that the larger the arc length difference, the greater the collapse rate of the payload space.

Method 2: The volume and inertia of the terminal bearing (3d) determine the spatial size of the inner frame structure (3o) and the outer frame structure (4o), that is, the distance between the inner frame tetrahedron or the outer frame tetrahedron body to the end angle. After adding the installation space such as the bearing and the rotating device, the parameter value of the inner rail arc radius r can be obtained. The key to the invention lies in the concentricity of the end shafts. Therefore, the greater the radius difference between the inner rail arc rod (1o) and the outer rail arc rod (2o), the more the geometric centripetality of each shaft core is ensured. However, the larger the parameter is, the larger the radial moment will be. The radial moment bearing capacity of the torque output device is weaker than the axial torque. Therefore, the parameter of the terminal arc (3c) radius r is set. For the value, the maximum balance between the geometric centripetal force of each end core and the radial moment of the torque output device shall be adopted.

Method 3: It is forbidden that the six angles between the corners of the inner corners of the inner frame and the six corners of the corners of the outer frame are completely equal, that is, the inner frame tetrahedron and the outer frame tetrahedron are not to be regular tetrahedrons. Because the tetrahedron is bound to appear four-axis singularity. Therefore, it is necessary to properly set the parameters such as the inner rail arc rod (1o), the outer rail arc rod (2o) arc length and the angle between the inner frame and the outer frame corner line to avoid the singular phenomenon. For example, the inner rail arc rod (1o) and the outer rail arc rod (2o) arc length should be avoided at the same time at right angles.

Method 4: Limit the steering path to avoid making the four corners of the inner frame no longer coincide with the four-corner line of the outer frame at the same time, so as to get rid of the singularity of the four-axis collinearity, but this will greatly limit the steering motion space. In order to make the terminal carrying (3d) of the present invention reach the preset running path, that is, the pre-ditch coordinate steering angle: the longitude angle and the latitude angle, the corner output value of each group of rotating devices (4a) must be calculated first. It is known that the outer frame (4o) four-corner core vector u first inputs the preset spherical coordinate longitude angle and latitude angle φ into the Euler angle conversion matrix, and obtains the inner frame of the new posture (3o) four-corner core vector v _i , according to The angle output value of the outer frame rotating device (4a) or the angle detecting device (3b) measured value, and the estimated value of the angle between the four inner rail arc bars (1o) and the outer rail arc bar (2o) is obtained. Estimate the center axis (2b) line vector w _i . The vector inner product of each inner core (1a), the middle core (2b) and the outer core (2a) is converted into a simultaneous polynomial, and the known or estimated parameter values are repeatedly superimposed to this. Establish a polynomial. Then carefully select the numerical method to obtain the output value of the corner demand of each set of torque output devices.

In summary, the analysis of possible interference and singular phenomena is thought to be The configuration parameters are selected according to the basis of the selection, and the design solution is proposed to affect the functional operation of the invention to ensure that the maximum spherical coordinate steering motion space is obtained.

(1)‧‧‧Internal rail arc group

(2) ‧‧‧ outer rail arc group

(3) ‧‧‧Internal frame structure and terminal bearer

(4) ‧‧‧Outer frame structure and frame rotating device

Claims (4)

A ball coordinate steering parallel mechanism comprises: an outer frame structure assembly, comprising an outer frame structure defined by a plurality of brackets, and four outer frame rotating devices disposed at preset positions of the outer frame structure, each outer frame rotating device The output axis defines an outer frame geometric tetrahedron, the output axis of each outer frame rotating device intersects at a central position of the preset outer frame structure; the inner frame structural assembly comprises an inner frame structure defined by a plurality of brackets And four inner frame rotating devices disposed at preset positions of the inner frame structure, wherein an output axis of each inner frame rotating device defines an inner frame geometric tetrahedron, and an output axis of each inner frame rotating device is intersected with the preset The center of the inner frame structure, and the center position of the inner frame coincides with the center position of the outer frame; the outer rail arc bar group includes four outer rail arc bars, and the outer ends of each outer rail arc bar are respectively connected with an external core The shaft is connected with the outer frame rotating device, and the inner end of the outer rail arc rod and the outer end of the inner rail arc rod are respectively connected by a middle connecting shaft core, and the outer shaft core and the middle connecting shaft core normally point to the center of the outer frame structure. , any two of the outer rails The sum of the arc lengths of the rods is greater than or equal to the sum of the angles of the two corners corresponding to the outer frame structure; the inner rail arc rod group includes four inner rail arc rods, and the inner ends of each inner rail arc rod are respectively bonded An inner connecting shaft core is axially connected with the inner frame rotating device, and the inner connecting shaft core normally points to the center of the inner frame structure, wherein the sum of the arc length angles of any two inner rail arc rods is greater than or equal to the corresponding two corner inner lines of the inner frame structure The sum of the included angles; and at least one terminal arc set, the terminal arc set has a terminal arc pole and a terminal load, and the terminal arc pole and any inner rail arc pole are coaxially mounted on the corner line of the inner frame structure In the upper end, the terminal arc rod is concentrically operated between the outer frame structure and each outer rail arc rod, and the terminal bearing is correspondingly installed at the outer end of the terminal arc rod. The ball coordinate of claim 1 is turned to a parallel mechanism, wherein the outer frame structure group is provided with an outer frame bracket; wherein the inner frame structure group is provided with an inner frame bracket. The ball coordinate of claim 1 is turned to a parallel mechanism, wherein the inner frame rotating device is any one of a torque output device, an angle detecting device, or a bearing; and the outer frame rotating device is a torque output device, an angle detecting device, or a bearing Any of them. The ball coordinate of claim 1 is turned to a parallel mechanism, wherein at least one of the inner frame rotating device and the outer frame rotating device axially connected to the inner rail and the outer rail arc of the same series is a torque output device, wherein the same group is The sum of the arc lengths of the inner rail and the outer rail arc is less than or equal to 180°.