CN107885916A - A kind of drill jumbo drill boom Analytical Methods of Kinematics based on CFDH methods - Google Patents

Abstract

The invention relates to a kinematics analysis method for a drill arm of a rock drilling rig based on a CFDH (Coordinate Fixed Denavit-Hartenberg) method. This method first determines the parameters of the connecting rod, including the size parameters of the connecting rod, including the length of the connecting rod and the torsion angle of the connecting rod, and the relationship parameters of the adjacent connecting rods, including the distance between the connecting rod and the joint rotation angle; then the drilling arm is simplified to the structure of a multi-joint robot , by setting the coordinate system of each member of the drill arm, determine the coordinate transformation matrix of the adjacent member, and then use the CFDH method to establish the kinematic equation of the drill arm of the rock drilling rig; finally use the kinematic equation established in MATLAB to draw the The effective working space of the drill arm of the rock rig. This method solves the difficult problem of determining the coordinate system in the study of the drill arm, and the establishment of the coordinate system group is intuitive and accurate, and provides an effective means for the kinematics analysis of the drill arm of the rock drilling rig.

Description

A Kinematics Analysis Method of Rock Drill Rig Arm Kinematics Based on CFDH Method

technical field

The invention relates to the field of engineering machinery kinematics analysis, in particular to a method for analyzing the kinematics of a drill arm of a rock drilling rig based on a CFDH method.

Background technique

Full hydraulic rock drilling jumbo is a large-scale rock drilling equipment integrating machinery, electricity and hydraulic pressure. It is an important machine tool for mines, tunnels and underground projects using the drilling and blasting method. Chassis etc. The fully hydraulic rock drilling jumbo can not only greatly reduce the physical labor of workers, improve construction conditions, and improve the efficiency of drilling operations, but also makes it easier to achieve high efficiency and automation in the actual construction process. Most of the hydraulic rock drilling equipment currently used in our country is imported from abroad, and most of them are expensive. If the hydraulic rock drilling rig is designed by itself, its cost will be greatly reduced compared with direct imports, and at the same time, the later maintenance costs and parts replacement will also be greatly reduced and facilitated. Because of this, the development of fully hydraulic rock drilling jumbo is of great significance to the modernization of manufacturing equipment in our country.

The drill arm of the fully hydraulic rock drilling rig is like the "arm" of the rock drilling rig, and is the core component of the rock drilling rig. The drill arm is the positioning mechanism for the rock drilling rig. The rock drilling rig can only The movement of joints can complete positioning, rock drilling and other actions. Therefore, in order to improve the efficiency, stability and safety performance of tunnel construction, it is imperative to study the drilling arm of the fully hydraulic rock drilling rig.

Contents of the invention

This application provides a method for analyzing the kinematics of the drill arm of the rock drilling rig based on the CFDH method, which solves the problem that the existing D-H analysis method cannot model all joint connecting rods, the established drill arm model is inconsistent with the entity, and the local joint position cannot be determined. analysis etc.

In order to achieve the above object, technical solution of the present invention is achieved in that way:

A method for analyzing the kinematics of the drill arm of a rock drilling rig based on the CFDH method, the method is realized through the following steps:

Step 1: Determine the connecting rod parameters, including the size parameters of the connecting rod: connecting rod length and connecting rod torsion angle; the relationship parameters of adjacent connecting rods: connecting rod distance and joint rotation angle;

Step 2: Establish the connecting rod coordinate system according to the CFDH method, and determine the coordinate transformation matrix of adjacent connecting rods

Step 3: Simplify the drill arm of the rock drilling rig into the structure of a multi-joint robot, and determine the coordinate transformation matrix of adjacent rods by setting the rod coordinate system. Multiply the coordinate transformation matrix of each rod in turn to obtain the relationship matrix between the end of the drill boom and the base, that is, the kinematic equation of the drill boom of the rock drilling rig;

Step 4: Input the kinematic equation of the drill arm of the rock drilling rig into MATLAB, and draw the effective working space of the drill arm of the rock drilling rig.

Further, the connecting rod parameters are determined in the step 1, and its specific steps are:

Step 1.1: Determine the dimensional parameters of the connecting rod

Link length a _i : the distance between the two joint axes i and i-1 along the common vertical line;

Connecting rod torsion angle α _i : the angle between the two joint axes i and i-1;

Step 1.2: Determine the relational parameters of adjacent links

Connecting rod distance d _i : the distance between two common vertical lines along the direction of joint axis i;

Joint rotation angle θ _i : the angle between two common vertical lines in a plane perpendicular to the joint axis.

Further, in the step 2, the link coordinate system is established, and the adjacent link coordinate transformation matrix is determined, and the specific steps are:

Step 2.1: Specify the coordinate axis X _i ; the coordinate axis Z _i ; the coordinate axis Y _i ; the coordinate origin O _i ;

Step 2.2: Establish the connecting rod coordinate system according to the CFDH method. Adjacent link coordinate transformation matrix is obtained by transforming the coordinate system {i-1} into the coordinate system {i} by four transformations, these four transformations are: rotate θ _i around the Z _i-1 axis; move d _i around the Z _i-1 axis; Move a _i along the X _i axis; rotate α _i along the X _i axis.

Further, in the step 3, the kinematics equation of the drill arm of the rock drilling rig is established, and the specific steps are:

Step 3.1: Simplify the drill arm of the rock drilling rig into the structure of a multi-joint robot, and establish the coordinate system group of the drill arm. In this coordinate system group, the base coordinate system {0} is set on the bottom plate of the drill arm, and the end coordinate system {7} It is set at the top of the drill rod; Step 3.2: Write the transformation matrix of each adjacent connecting rod according to the actual measurement data: Multiply the transformation matrices in turn to obtain the relationship matrix between the end of the drill arm and the base, that is, the kinematic equation of the drill arm of the rock drilling rig

Step 3.3: Substitute the initial values of each joint into the kinematic equation to verify whether the kinematic equation is correct.

Further, the step 4 draws the effective working space of the drill arm of the rock drilling rig as follows:

Step 4.1: Use MATLAB software to program, so that each joint variable randomly selects a value within the value range, and substitutes it into the kinematic equation, thereby obtaining the three-dimensional coordinate value of the end point of the drill arm;

Step 4.2: Use the plot function to output the three-dimensional coordinate points into a graph, and then obtain the three-dimensional result of the graphical workspace.

Compared with the prior art, the beneficial effects of the present invention are as follows:

The invention is applied to the kinematics analysis of the drill arm of the rock drilling rig, and uses a D-H representation method—CFDH method in which the coordinate system is fixed on the entity, which solves the problem of difficult determination of the coordinate system in the study of the drill arm, and the coordinate system group The establishment is more intuitive and accurate. The invention not only improves the accuracy and operability of the kinematics analysis, but also saves the analysis time, and provides an effective analysis means for optimizing and improving the rock drilling jumbo.

Description of drawings

The flowchart of Fig. 1 analytical method of the present invention;

Fig. 2 is a schematic diagram of the coordinate system of the drill arm connecting rod;

Figure 3 is a real shot of a certain type of full hydraulic rock drilling rig;

Fig. 4 is a schematic diagram of the coordinate system group of the drill arm of the rock drilling rig;

Fig. 5 is a three-dimensional schematic diagram of the working space of the drill arm of the rock drilling rig;

Fig. 6 is a schematic diagram of the projection of the working space on the XY plane;

Detailed ways

The present invention will be further described in detail below through specific embodiments in conjunction with the accompanying drawings. Wherein, similar elements in different implementations adopt associated similar element numbers. In the following implementation manners, many details are described for better understanding of the present application. However, those skilled in the art can readily recognize that some of the features can be omitted in different situations, or can be replaced by other elements, materials, and methods. In some cases, some operations related to the application are not shown or described in the description, this is to avoid the core part of the application being overwhelmed by too many descriptions, and for those skilled in the art, it is necessary to describe these operations in detail Relevant operations are not necessary, and they can fully understand the relevant operations according to the description in the specification and general technical knowledge in the field.

In addition, the characteristics, operations or characteristics described in the specification can be combined in any appropriate manner to form various embodiments. At the same time, the steps or actions in the method description can also be exchanged or adjusted in a manner obvious to those skilled in the art. Therefore, various sequences in the specification and drawings are only for clearly describing a certain embodiment, and do not mean a necessary sequence, unless otherwise stated that a certain sequence must be followed.

The serial numbers assigned to components in this document, such as "first", "second", etc., are only used to distinguish the described objects, and do not have any sequence or technical meaning. The "connection" and "connection" mentioned in this application all include direct and indirect connection (connection) unless otherwise specified.

The present invention provides a method for analyzing the kinematics of the drill arm of a rock drilling rig based on the CFDH method. As shown in Figure 1, the method is implemented through the following steps:

Step 1: Determine the connecting rod parameters, including the size parameters of the connecting rod: connecting rod length and connecting rod torsion angle; the relationship parameters of adjacent connecting rods: connecting rod distance and joint rotation angle;

Step 2: Establish the connecting rod coordinate system according to the CFDH method, and the coordinate transformation matrix of adjacent connecting rods It is obtained by four transformations from the coordinate system {i-1} to the coordinate system {i};

Step 3: Simplify the drill arm of the rock drilling rig into the structure of a multi-joint robot, and determine the coordinate transformation matrix of adjacent members by setting the coordinate system of each member of the drill arm. Multiply the coordinate transformation matrix of each rod in turn to obtain the relationship matrix between the end of the drill boom and the base, that is, the kinematic equation of the drill boom of the rock drilling rig;

Step 4: Input the kinematic equation of the drill arm of the rock drilling rig into MATLAB, and draw the effective working space of the drill arm of the rock drilling rig.

Taking a certain type of rock drilling jumbo as an example, the specific implementation steps of a method for analyzing the kinematics of the drilling jumbo based on the CFDH method of the present invention are described below:

Step 1: Determine the connecting rod parameters, including the size parameters of the connecting rod: connecting rod length and connecting rod torsion angle; the relationship parameters of adjacent connecting rods: connecting rod distance and joint rotation angle;

The drill arm can be considered as a mechanical arm with multiple links connected by joints. In the CFDH method, the specifications of the connecting rod parameters are as follows:

(1) Dimensional parameters of the connecting rod

Link length a _i : the distance between the two joint axes i and i-1 along the common vertical line;

Connecting rod torsion angle α _i : the angle between the two joint axes i and i-1;

(2) The relationship parameters of adjacent connecting rods

Connecting rod distance d _i : the distance between two common vertical lines along the direction of joint axis i;

Joint rotation angle θ _i : the angle between two common vertical lines in a plane perpendicular to the joint axis.

Step 2: Establish the connecting rod coordinate system and the adjacent connecting rod coordinate transformation matrix;

(1) Specify the coordinate axis and coordinate origin

Coordinate axis X _i : the common vertical line along the axes of the two joints of link i-1 points to joint i;

Coordinate axis Z _i : coincides with the axis of joint i;

Coordinate axis Y _i : determined according to the rule of the right-hand rectangular coordinate system.

Coordinate origin O _i : when the joint axis i-1 intersects with the joint axis i, take the intersection point of the two axes; Intersection point: when the joint axis i-1 is parallel to the joint sweat axis i, take the intersection point of the common perpendicular line between the joint axis i and the joint axis i-1 and the joint axis i.

The establishment of the connecting rod coordinate system and the specification of parameters are shown in Figure 2.

(2) According to the CFDH method, the coordinate system of the connecting rod is established, and the coordinate transformation matrix of adjacent connecting rods Four transformations from the coordinate system {i-1} to the coordinate system {i} are obtained:

Rotate θ _i around Z _i-1 axis: Rot(Z _i-1 ,θ _i )

Move d _i along Z _i-1 axis: Trans(Z _i-1 ,d _i )

Move a _i along the X _i axis: Trans(X _i ,a _i )

Rotate α _i around the X _i axis: Rot(X _i ,α _i )

The CFDH parameters of the rotating link are a _i , α _i , d _i , θ _i , where the joint rotation angle θ _i is the joint variable, and the link length a _i , link torsion angle α _i , and link distance d _i are fixed of. These four parameters determine the pose of link i relative to link i-1, that is, the coordinate transformation matrix is As shown in formula 1.

Step 3: Establish the kinematics equation of the drill arm of the rock drilling rig

(1) Figure 3 is a real shot of a certain type of rock drilling rig. The drill arm of the rock drilling rig is simplified into the structure of a multi-joint robot, and the coordinate system group of the drill arm is established. In this coordinate system group, the base coordinate system {0} It is set on the bottom plate of the drill arm, and the end coordinate system {7} is set on the top of the drill rod.

(2) Figure 4 is the coordinate system group of the drill boom of a certain type of rock drilling rig, and the transformation matrix of each adjacent connecting rod is written according to the actual measurement data: Multiply the transformation matrix in turn to obtain the relationship matrix between the end of the drill arm and the base and the kinematic equation of the drill arm of the rock drilling rig

According to the actual measurement data provided by a certain company:

a ₁ =270mm; a ₂ =3100mm; a ₄ =1240mm; a ₆ =460mm;

d ₃ =220 mm; d ₄ =1280 mm; d ₅ =950 mm; d ₆ =545 mm.

Combining the following table 1 and formula 1, the transformation matrix between the connecting rods of the drill arm can be obtained.

Note: si=sinθ _i , ci=cosθ _i (i=1,2,3,4,5,6)

Table 1

(3) Multiply the above matrices in turn to obtain the relationship matrix between the end of the drill arm and the base and the kinematic equation of the drill arm of the rock drilling rig.

To describe the relationship of one coordinate system relative to another coordinate system, the origin position of the coordinate system and the direction of its coordinate axes must be given. In formula (9), p is the position of the end of the drill arm; n is the cosine of the direction of the principal vector of the X-axis; o is the cosine of the direction of the principal vector of the Y-axis; a is the cosine of the direction of the principal vector of the Z-axis. According to the content of the CFDH method, use n _x , _ny , _nz , o _x , o y , o _z , a _x , a _y , _{a z to} represent the pose of the end effector of the manipulator, and use p _x , p _y , p _z to represent the position of the end effector of the manipulator.

(4) According to the actual measurement data provided by a certain company, in the initial state of the drill arm

p _x =6300mm, p _y =-750mm, p _z =5200mm.

In order to verify whether the result is correct, take the initial values of each joint θ ₀ = θ ₁ = θ ₂ = θ ₅ = θ ₆ = 0°; θ ₃ = θ ₄ = 90°; d ₇ = 3000mm; l ₁ = 0mm. Calculated by CFDH method: p _x =6330mm, p _y =-739mm, p _z =5230mm.

According to regulations, the error of the actual measurement and calculation results is within 5%, indicating that the kinematic equations are established correctly. It can be seen from Table 2 below that the error of the actual measurement and calculation results is much smaller than the specified error range, which shows that the kinematic equation of the drill arm is established correctly.

Table 2

Step 4: Map the effective working space of the drill rig's boom

(1) Use MATLAB software to program, so that each joint variable randomly selects a value within the value range, and substitutes it into the kinematic equation, thereby obtaining the three-dimensional coordinate value of the end point of the drill arm;

(2) Use the plot function to output the three-dimensional coordinate points into a graph, and then obtain the three-dimensional result of the graphical workspace. Using the for loop to randomly select such 15,000 points can form a highly intuitive working space diagram of the drill arm. The random joint variable is obtained by the following formula:

θ _i ＝θ _i ^min +(θ _i ^max -θ _i ^min )×rand(1) (10)

In the above formula, θ _i ^min is the minimum value of the rotation range of joint i; θ _i ^max is the maximum value of the rotation range of joint i; rand(1) refers to randomly selecting a number between 0 and 1.

(3) The set of spatial positions reached by the movement of the end of the drill rod is the working space of the drilling arm. Figure 5 is a three-dimensional diagram of the working space of the drilling arm. In the process of rock drilling, the most concerned drilling area on the face, that is, the projection of the working space of the drill arm on the XY plane, can be seen from Figure 6, the distribution of the projection points on the XY plane is a fan, and the data analysis can be It can be seen that it is a similar sector with a sector radius of 0.9×104 mm, which meets the requirements for the use of rock drilling rigs.

The above uses specific examples to illustrate the present invention, which is only used to help understand the present invention, and is not intended to limit the present invention. For those skilled in the technical field to which the present invention belongs, some simple deduction, deformation or replacement can also be made according to the idea of the present invention.

Claims (5)

1. a kind of drill jumbo drill boom Analytical Methods of Kinematics based on CFDH methods, it is characterised in that this method passes through following step It is rapid to realize：

Step 1：Link parameters are determined, the link parameters include the dimensional parameters of connecting rod and the Relation Parameters of adjacent links；Even The dimensional parameters of bar include length of connecting rod and connecting rod torsional angle；The Relation Parameters of adjacent links include connecting rod distance and joint rotation angle；

Step 2：Link rod coordinate system is established according to CFDH methods, determines adjacent links transformation matrix of coordinates

Step 3：Drill jumbo drill boom is reduced to the structure of articulated robot, by setting member coordinates, determined adjacent The transformation matrix of coordinates of rod member；The transformation matrix of coordinates of each rod member is multiplied successively, obtains relation square of the drill boom end to pedestal Battle array is drill jumbo drill boom kinematical equation；

Step 4：The kinematical equation of drill jumbo drill boom is input in MATLAB, draws out effective work of drill jumbo drill boom Make space.

2. analysis method according to claim 1, it is characterised in that determine link parameters in the step 1, its specific step Suddenly it is：

Step 1.1：Determine the dimensional parameters of connecting rod

Length of connecting rod a_i：Distances of two joints axes i and i-1 along common vertical line；

Connecting rod torsional angle α_i：Two joints axes i and i-1 angle；

Step 1.2：Determine the Relation Parameters of adjacent links

Connecting rod distance d_i：Along joints axes i directions, the distance between two common vertical lines；

Joint rotation angle θ_i：In the plane of joints axes, the angle between two common vertical lines.

3. analysis method according to claim 1 or 2, it is characterised in that link rod coordinate system is established in the step 2, really Determine adjacent links transformation matrix of coordinates, it is concretely comprised the following steps：

Step 2.1：Provide reference axis X_i；Reference axis Z_i；Reference axis Y_i；Origin of coordinates O_i；

Step 2.2：Link rod coordinate system is established according to CFDH methods.Adjacent links transformation matrix of coordinatesIt is by coordinate system { i-1 } Be transformed into coordinate system { i } four convert what is obtained, and this four conversion are respectively：Around Z_i-1Axle turns θ_i；Around Z_i-1Axle moves d_i；Edge X_iAxle moves a_i；Along X_iAxle turns α_i。

4. analysis method according to claim 3, it is characterised in that the motion of drill jumbo drill boom is established in the step 3 Equation is learned, it is concretely comprised the following steps：

Step 3.1：Drill jumbo drill boom is reduced to the structure of articulated robot, establishes drill boom coordinate system group, this coordinate system Basis coordinates system { 0 } is located at drill boom bottom plate in group, end coordinate system { 7 } is then located at the top of drill steel.

Step 3.2：The transformation matrix of each adjacent links is write out according to actual measurement data： Transformation matrix is multiplied successively, drill boom end is obtained and the relational matrix i.e. drill jumbo drill boom of pedestal is transported It is dynamic to learn equation

Step 3.3：Each joint initial value is taken to substitute into kinematical equation, whether checking kinematical equation is correct.

5. analysis method according to claim 4, it is characterised in that described step 4 draws having for drill jumbo drill boom Imitating working space is specially：

Step 4.1：Using MATLAB software programmings, each joint variable is randomly selected the value in span, substituted into fortune It is dynamic to learn in equation, thus obtain the D coordinates value of drill boom distal point；

Step 4.2：Three-dimensional coordinate point is exported into figure using plot functions, has just obtained the patterned three-dimensional knot of working space Fruit.