CN113624400A - Method for measuring mass center of object in large-space rope drive assembly process - Google Patents

Method for measuring mass center of object in large-space rope drive assembly process Download PDF

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CN113624400A
CN113624400A CN202110960260.3A CN202110960260A CN113624400A CN 113624400 A CN113624400 A CN 113624400A CN 202110960260 A CN202110960260 A CN 202110960260A CN 113624400 A CN113624400 A CN 113624400A
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coordinate system
rope
tool
mass center
measuring
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CN113624400B (en
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孙光辉
卢彦岐
姚蔚然
吴立刚
高亚斌
刘健行
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

A method for measuring the mass center of an object in a large-space rope-driven assembly process belongs to the field of assembly and measurement of rope-driven robots. The traditional measuring method has the problems that measuring equipment is various and a separate measuring device is needed for measurement. The method firstly calculates the tension of each rope in 6 ropes connected with a circular tool in an O-shaped mode0‑X0Y0Z0Direction vector T in coordinate system0iAnd in O1‑X1Y1Z1Direction vector T in coordinate system1i(ii) a Respectively measuring the tension values F of 6 ropes through tension sensors1iAnd is in X1Axis, Y1Axis and Z1Decomposing on the shaft; gravity G of circular tool0Decomposition to X1Axis, Y1Axis and Z1On the shaft, and obtaining the mass center of the tool at O based on a moment balance equation1‑X1Y1Z1Coordinates of a coordinate system; then the round tool is connected with the assembled object as a wholeThe mass center of the whole body consisting of the tool and the assembled object is obtained in the same way at O2‑X2Y2Z2Coordinates of a coordinate system; finally, obtaining M through the centroid theorempThe coordinates of (a). The method is mainly used for measuring the mass center of an object in the rope driving assembly process.

Description

Method for measuring mass center of object in large-space rope drive assembly process
Technical Field
The invention belongs to the field of assembly and measurement of rope-driven robots, and particularly relates to a method for measuring the mass center of an object in the process of rope-driven assembly.
Background
Along with the rapid development of production economy, industry, aerospace industry, big space assembly problem becomes main assembly problem gradually, therefore has the advantage that can big space deployment because the unique flexible characteristic of rope to it gradually becomes the development trend to use rope to drive rigging equipment to carry out big space assembly, and rope drives rigging equipment and for disposing one set of rope controlling means respectively in a plurality of positions in big space, and wherein rope controlling means includes motor and rope pay-off and take-up device. Each set of rope control device respectively stretches out a rope to be connected to a connecting point of the tool, the tool is connected with an object to be assembled, and the tail end of the assembled object is controlled to move to a specified position by cooperatively controlling the winding and unwinding of each rope. During the assembly process, it is necessary to measure mass characteristics of the assembled object, such as the center of mass of the object. Only by knowing the mass center position of each single assembled object, the mass center position of the whole assembled object can be calculated, and subsequent research and application can be carried out. The traditional measuring method needs to respectively measure the centroid position of an object through a set of independent measuring device before assembly, then the rope-driven assembly equipment is used for assembling the object to the expected position in the expected posture, namely the traditional method for measuring the centroid of the object needs to use an independent measuring platform for measurement and needs to manually turn over the object to be measured to measure the centroid. Therefore, the conventional method has a lot of measuring devices, needs a separate measuring device to measure, measures the quality characteristics at random positions on the ground, and may have certain deviation, which is not the result of measurement in a real working environment and state.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the mass center position of an object is measured by a set of independent measuring devices before assembly in the conventional measuring method, and then the object is assembled to a desired position in a desired posture by using rope-driven assembling equipment, so that the conventional measuring method has various measuring devices, needs the independent measuring devices for measurement, measures the quality characteristics at random positions on the ground, does not obtain the measurement result in a real working environment and state, and possibly has certain deviation; further provides a method for measuring the mass center of an object in the large-space rope-drive assembly process;
the technical scheme adopted by the invention for solving the technical problems is as follows:
a method for measuring the mass center of an object in a large-space rope drive assembly process comprises the following steps:
s1: measuring the mass center of the tool:
s1.1: establishing a coordinate system O0-X0Y0Z0And a coordinate system O1-X1Y1Z1；
S1.2: the rope drives the rigging equipment and evenly is connected to circular frock through 6 ropes, utilizes the rope to drive the rigging equipment with X circular frock0Rotating the shaft by an angle alpha and keeping the shaft still; at this time, a rope exit point C between the rope drive rigging equipment and the ropeiRelative to O0-X0Y0Z0The coordinates of the coordinate system are (x)c0i,yc0i,zc0i) I is 1,2,3,4,5, 6; rope traction point P between circular tool and ropeiRelative to O0-X0Y0Z0The coordinates of the coordinate system are (x)p0i,yp0i,zp0i)；
S1.3: respectively calculating the tension of each rope in 6 ropes connected with the circular tool at the position O0-X0Y0Z0Direction vector T in coordinate system0iAnd in O1-X1Y1Z1Direction vector T in coordinate system1i；
S1.4: respectively calculating rope pulling points P of 6 ropes connected with the circular tooliAt O1-X1Y1Z1Coordinates (x) in a coordinate systemp1i,yp1i,zp1i)；
S1.5: respectively measuring the tension values F of 6 ropes through tension sensors1iAnd the tension of each rope is respectively decomposed into O1-X1Y1Z1X of a coordinate system1Axis, Y1Axis and Z1On the shaft and respectively obtain F1ix,F1iy,F1iz；
S1.6: center of mass M of circular toolsRelative to O1-X1Y1Z1The coordinates of the coordinate system are (x)ms1,yms1,zms1) Gravity G of the circular tool0Decomposition to O1-X1Y1Z1X of a coordinate system1Axis, Y1Axis and Z1On the shaft and get G01x,G01y,G01zIt can be obtained by the following formula:
Figure BDA0003221807870000021
wherein m represents the center of mass of the circular tool, s represents the whole tool, and 1 represents O1-X1Y1Z1The established coordinate system is a reference system;
s1.7: respectively establishing X1Axis, Y1Axis and Z1The moment balance equation of the shaft can be obtained by the following formula:
Figure BDA0003221807870000022
s1.8: the centroid M of the tool can be obtained by solving the triaxial moment balance equation in the step S1.7sRelative to O1-X1Y1Z1Coordinates (x) of a coordinate systemms1,yms1,zms1)；
S2: measuring the center of mass of the tool and the assembled object as a whole:
s2.1: establishing a coordinate system O2-X2Y2Z2；
S2.2: the rope drives the rigging equipment and evenly is connected to circular frock through 6 ropes, and the circular frock is connected and is assembled the object, utilizes the rope to drive the whole of rigging equipment with centre of a circle frock and assembled the object and constitute with X0Rotating the shaft by an angle alpha and keeping the shaft still; at this time, a rope exit point C between the rope drive rigging equipment and the ropeiRelative to O0-X0Y0Z0The coordinates of the coordinate system are (x)c0i,yc0i,zc0i) (ii) a Rope traction P between circular tool and ropeiRelative to O0-X0Y0Z0The coordinate of the coordinate system is (x'p0i,y′p0i,z′p0i)；
S2.3: respectively calculating the tension of each rope in 6 ropes of the connecting tool at O0-X0Y0Z0Direction vector T 'under coordinate system'0iIn O1-X1Y1Z1Direction vector T 'under coordinate system'1iAnd in O2-X2Y2Z2Direction vector T 'under coordinate system'2i；
S2.4: respectively calculating each rope traction point P of 6 ropes connected with the circular tooliAt O1-X1Y1Z1Coordinate (x ') in coordinate system'p1i,y′p1i,z′p1i) And in O2-X2Y2Z2Coordinate (x ') in coordinate system'p2i,y′p2i,z′p2i)；
S2.5: measuring the tension value F of 6 ropes through a tension sensor2iAnd the tension of each rope is respectively decomposed into O2-X2Y2Z2X of a coordinate system2Axis, Y2Axis, Z2On the shaft and respectively obtain F2ix,F2iy,F2iz；
S2.6: center of mass M of circular tool and assembled objecteRelative to O2-X2Y2Z2The coordinates of the coordinate system are (x)me2,yme2,zme2) Gravity G of the whole body consisting of the tool and the assembled object1Decomposition to O2-X2Y2Z2X of a coordinate system2Axis, Y2Axis, Z2On the shaft to obtain G12x,G12y,G12zIt can be obtained by the following formula:
Figure BDA0003221807870000031
wherein m represents the mass center, e represents the whole of the circular tool and the assembled object, and 2 represents O2-X2Y2Z2The established coordinate system is a reference system;
s2.7: respectively establishing X2Axis, Y2Axis, Z2The moment balance equation of (a) can be obtained by the following formula:
Figure BDA0003221807870000041
s2.8: the integral mass center M formed by the tool and the assembled object can be obtained by solving the triaxial moment balance equation in the step S2.7eRelative to O2-X2Y2Z2Coordinates (x) of a coordinate systemme2,yme2,zme2)；
S3: calculating the mass center of the assembled object:
s3.1: calculate the mass center M of the round frocksRelative to O2-X2Y2Z2Coordinates (x) of a coordinate systemms2,yms2,zms2) It can be obtained by the following formula:
Figure BDA0003221807870000042
Figure BDA0003221807870000043
s3.2: setting mass center M of assembled objectpRelative to O2-X2Y2Z2The coordinates of the coordinate system are (x)mp2,ymp2,zmp2) Finding M by centroid theorempCoordinate (x) ofmp2,ymp2,zmp2) It can be obtained by the following formula:
Figure BDA0003221807870000044
wherein m represents the centroid, p represents the whole of the object to be assembled, and 2 represents O2-X2Y2Z2The coordinate system established is the reference system.
Further, in S1.1, O is0-X0Y0Z0The coordinate system is a world coordinate system of the assembly space of the rope drive assembly equipment;
the coordinate system O1-X1Y1Z1Is obtained by the following steps: establishing a space coordinate system by taking the center of the circular tool as an original point, and winding the space coordinate system in parallel by X0Obtaining a coordinate system O by rotating the shaft by an angle alpha1-X1Y1Z1。
Further, in S1.3, the direction vector T0iObtained by the following formula:
Figure BDA0003221807870000051
Figure BDA0003221807870000052
wherein, c is the rope outlet point of the belt meter, p is the rope drawing point, 0 is O0-X0Y0Z0The established world coordinate is a reference system, and i represents the ith rope connected with the tool on the rope drive assembly equipment;
the direction vector T1iObtained by the following formula:
T0i＝R′x(α)T1i+D′01
Figure BDA0003221807870000053
Figure BDA0003221807870000054
D′01is a translation conversion matrix, R'x(α) is a rotation transformation matrix, x1,y1,z1Are each O1-X1Y1Z1Origin of coordinate system is O0-X0Y0Z0Coordinate values on the X, Y and Z axes in the coordinate system.
Further, in S1.4, the rope pulling point Pi(i ═ 1,2,3,4,5,6) in O1-X1Y1Z1Coordinates (x) in a coordinate systemp1i,yp1i,zp1i) Obtained by the following formula:
Figure BDA0003221807870000055
Figure BDA0003221807870000056
Figure BDA0003221807870000061
D01for translating the transformation matrix, RxAnd (alpha) is a rotation transformation matrix.
Further, in S2.1, the coordinate system O2-X2Y2Z2Is obtained by the following steps: establishing a space coordinate system by taking any vertex or central point of the assembled object as an origin, wherein the coordinate values of the space coordinate system and a coordinate system O0-X0Y0Z0Equidirectional, space coordinate system surrounding X0Obtaining a coordinate system O by rotating the shaft by an angle alpha2-X2Y2Z2。
Further, in S2.3, the direction vector T'0iObtained by the following formula:
Figure BDA0003221807870000062
Figure BDA0003221807870000063
wherein, c is the rope outlet point of the belt meter, p is the rope drawing point, 0 is O0-X0Y0Z0The established world coordinate is a reference system, and i represents the ith rope of the rope drive assembly equipment connecting tool;
the direction vector T'1iObtained by the following formula:
T′0i＝R′x(α)T′1i+D′01
Figure BDA0003221807870000064
Figure BDA0003221807870000065
D′01is a translation conversion matrix, R'x(α) is a translation and rotation transformation matrix;
the direction vector T'2iObtained by the following formula:
T′1i＝T′2i+D′12
Figure BDA0003221807870000071
D′12converting the matrix for translation; x is the number oflRepresents O2-X2Y2Z2The origin of the coordinate system is at O1-X1Y1Z1In the coordinate system at X1Coordinate value of axial direction, ylRepresents O2-X2Y2Z2The origin of the coordinate system is at O1-X1Y1Z1In the coordinate system at Y1Coordinate values in the axial direction, wherein h represents O2-X2Y2Z2Origin of coordinate system relative to O1-X1Y1Z1Origin of the coordinate system is along Z1Distance of the shaft.
Further, in S2.4, the rope pulling point PiAt O1-X1Y1Z1Coordinate (x ') in coordinate system'p1i,y′p1i,z′p1i) Obtained by the following formula:
Figure BDA0003221807870000072
Figure BDA0003221807870000073
Figure BDA0003221807870000074
wherein p represents a rope pulling point, 1 represents O1-X1Y1Z1The coordinate system is established as a reference system, i represents the ith rope connected with the workpiece;
the rope traction point Pi(i ═ 1,2,3,4,5,6) in O2-X2Y2Z2Coordinate (x ') in coordinate system'p2i,y′p2i,z′p2i) Obtained by the following formula:
Figure BDA0003221807870000075
Figure BDA0003221807870000076
D12converting the matrix for translation; wherein p represents a rope pulling point, 2 represents O2-X2Y2Z2The coordinate system established is a reference system, i represents the ith rope connected with the tool.
Further, in S1.5, F is1ix,F1iy,F1izObtained from the following equation:
Figure BDA0003221807870000081
further, in S2.5, F2ix,F2iy,F2izObtained from the following equation:
Figure BDA0003221807870000082
furthermore, circular frock include disc (1), adapting unit (2) disc (1) on evenly open and to have 6 rope traction holes, adapting unit (2) set up on disc (1) for connect by the assembly object.
Compared with the prior art, the invention has the following beneficial effects:
the measuring method can use one set of equipment to complete the measuring and assembling tasks at the same time, not only does not need excessive measuring equipment, but also does not need a separate measuring device, and the measuring method is convenient to measure; meanwhile, the invention measures the assembled object in the state close to the actual working state, and can accurately measure the mass center and the mass characteristic of the object.
The main advantages are mainly focused on the following points:
(1) the method simplifies and optimizes the traditional method for measuring the centroid of the object, does not need to use a separate centroid measuring device, does not need to obtain three coordinates of the centroid after artificially turning the object, and can directly measure the three coordinates of the centroid of the object at one time.
(2) The centroid measuring task of the assembled object and the assembling task of moving the assembled object to a desired position in a cross-space mode can be completed by using one set of rope driving equipment, the task which can be realized by adding one set of measuring device and one set of assembling device in the prior art is realized, the use cost is reduced, and the work efficiency is improved.
(3) The reason why the measurement of the mass center of the object is completed in the assembling process is that the actual working state of the assembled object is closer to the assembling process, so that the measured quality characteristic is more suitable for an actual assembly body.
Drawings
FIG. 1 is a schematic view of the overall structure of a rope-driven assembly device for measuring the mass center of an object;
fig. 2 is a flow chart of the rope-driven assembling equipment for measuring the mass center of an object.
Detailed Description
The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings:
the method for measuring the mass center of the object in the large-space rope drive assembly process comprises the following specific measurement steps:
s1: measuring the mass center of the tool:
s1.1: establishing a coordinate system O0-X0Y0Z0And a coordinate system O1-X1Y1Z1: said O is0-X0Y0Z0The coordinate system is a world coordinate system of the assembly space of the rope drive assembly equipment; establishing a space coordinate system (earth coordinate system) by taking the center of the circular tool as an original point, wherein the space coordinate system (earth coordinate system) winds X0Obtaining a coordinate system O by rotating the shaft by an angle alpha1-X1Y1Z1；
The rope drive assembly device in this embodiment may be implemented by applying the following patent application No. 202010973897.1: an overhead multi-degree-of-freedom rope-driven parallel robot, or application number: 202010973880.6, the patent names: the rope winding mechanism and the multi-degree-of-freedom rope-driven parallel robot using the rope winding mechanism are arranged in parallel; wherein, the rope in the rope drive assembling equipment is a rope with higher rigidity.
The circular tool comprises a disc 1 and a connecting part 2, wherein 6 rope drawing holes are uniformly formed in the circumferential surface of the disc 1, and the connecting part 2 is arranged on the disc 1 and used for connecting an assembled object; the disc may be a ring or the like, and the coupling member may be a gripper or the like.
S1.2: the rope drives the rigging equipment and evenly is connected to circular frock through 6 ropes, utilizes the rope to drive the rigging equipment with X circular frock0Rotating the shaft by an angle alpha and keeping the shaft still; at this time, a rope exit point C between the rope drive rigging equipment and the ropei(i ═ 1,2,3,4,5,6) relative to O0-X0Y0Z0The coordinates of the coordinate system are (x)c0i,yc0i,zc0i) (ii) a Rope traction point P between circular tool and ropei(i ═ 1,2,3,4,5,6) relative to O0-X0Y0Z0The coordinates of the coordinate system are (x)p0i,yp0i,zp0i)；
S1.3: respectively calculating the tension of each rope in 6 ropes of the connecting tool at O0-X0Y0Z0Direction vector T in coordinate system0i(i ═ 1,2,3,4,5,6), by the following formula:
Figure BDA0003221807870000091
Figure BDA0003221807870000092
wherein liIs the intermediate variable(s) of the variable,c the rope exit point of the belt meter, p represents the rope pulling point, 0 represents O0-X0Y0Z0The established world coordinate is a reference system, and i represents the ith rope connected with the tool on the rope drive assembly equipment;
s1.4: respectively calculating the tension of each rope in 6 ropes of the connecting tool at O1-X1Y1Z1Direction vector T in coordinate system1iObtained by the following formula:
T0i＝R′x(α)T1i+D′01 (3)
Figure BDA0003221807870000101
Figure BDA0003221807870000102
D′01is a translation conversion matrix, R'x(α) is a rotation transformation matrix, x1,y1,z1Are each O1-X1Y1Z1The origin of the coordinate system (the central point of the circular tool) is O0-X0Y0Z0Coordinate values on an X-axis, a Y-axis, and a Z-axis in a coordinate system;
s1.5: respectively calculating rope pulling points P of 6 ropes connected with the circular tooli(i ═ 1,2,3,4,5,6) in O1-X1Y1Z1Coordinates (x) in a coordinate systemp1i,yp1i,zp1i) Obtained by the following formula:
Figure BDA0003221807870000103
Figure BDA0003221807870000104
Figure BDA0003221807870000105
D01for translating the transformation matrix, RxAnd (alpha) is a rotation transformation matrix.
S1.6: respectively measuring the tension values F of 6 ropes through tension sensors1i(i ═ 1,2,3,4,5,6), and the tension of each rope is resolved to O1-X1Y1Z1X of a coordinate system1Axis, Y1Axis and Z1On the shaft and respectively obtain F1ix,F1iy,F1izIt can be obtained by the following formula:
Figure BDA0003221807870000106
s1.7: center of mass M of circular toolsRelative to O1-X1Y1Z1The coordinates of the coordinate system are (x)ms1,yms1,zms1) Gravity G of the circular tool0Decomposition to O1-X1Y1Z1X of a coordinate system1Axis, Y1Axis and Z1On the shaft and get G01x,G01y,G01zIt can be obtained by the following formula:
Figure BDA0003221807870000111
wherein m represents the center of mass of the circular tool, s represents the whole tool, and 1 represents O1-X1Y1Z1The established coordinate system is a reference system;
s1.8: respectively establishing X1Axis, Y1Axis and Z1The moment balance equation of the shaft can be obtained by the following formula:
Figure BDA0003221807870000112
s1.9: the centroid M of the tool can be obtained by solving the three-axis moment balance equation (11)sRelative to O1-X1Y1Z1Coordinates (x) of a coordinate systemms1,yms1,zms1)；
S2: measuring the center of mass of the tool and the assembled object as a whole:
s2.1: establishing a coordinate system O2-X2Y2Z2: establishing a space coordinate system by taking any vertex or central point of the assembled object as an origin, wherein the coordinate values of the space coordinate system and a coordinate system O0-X0Y0Z0Equidirectional, space coordinate system surrounding X0Obtaining a coordinate system O by rotating the shaft by an angle alpha2-X2Y2Z2；
S2.2: the rope drives the rigging equipment and evenly is connected to circular frock through 6 ropes, and circular frock passes through adapting unit and connects and is assembled the object, utilizes the rope to drive the whole of rigging equipment with centre of a circle frock and assembled the object and constitute with X0Rotating the shaft by an angle alpha and keeping the shaft still; at this time, a rope exit point C between the rope drive rigging equipment and the ropei(i ═ 1,2,3,4,5,6) relative to O0-X0Y0Z0The coordinates of the coordinate system are (x)c0i,yc0i,zc0i) (ii) a Rope traction P between circular tool and ropei(i ═ 1,2,3,4,5,6) relative to O0-X0Y0Z0The coordinate of the coordinate system is (x'p0i,y′p0i,z′p0i)；
S2.3: respectively calculating the tension of each rope in 6 ropes of the connecting tool at O0-X0Y0Z0Direction vector T 'under coordinate system'0iObtained by the following formula:
Figure BDA0003221807870000121
Figure BDA0003221807870000122
wherein li' is an intermediate variable, c is a rope outlet point, p is a rope drawing point, 0 is O0-X0Y0Z0The established world coordinate is a reference system, and i represents the ith rope of the rope drive assembly equipment connecting tool.
S2.4: respectively calculating the tension of each rope in 6 ropes of the connecting tool at O1-X1Y1Z1Direction vector T 'under coordinate system'1iObtained by the following formula:
T′0i＝R′x(α)T′1i+D′01 (14)
Figure BDA0003221807870000123
Figure BDA0003221807870000124
D′01is a translation conversion matrix, R'x(α) is a translation and rotation transformation matrix;
s2.5: respectively calculating the tension of each rope in 6 ropes of the connecting tool at O2-X2Y2Z2Direction vector T 'under coordinate system'2iObtained by the following formula:
T′1i＝T′2i+D′12 (17)
Figure BDA0003221807870000125
D′12converting the matrix for translation; x is the number oflRepresents O2-X2Y2Z2The origin of the coordinate system is at O1-X1Y1Z1In the coordinate system at X1Coordinate value of axial direction, ylRepresents O2-X2Y2Z2The origin of the coordinate system is at O1-X1Y1Z1In the coordinate system at Y1Coordinate values in the axial direction, wherein h represents O2-X2Y2Z2Origin of coordinate system relative to O1-X1Y1Z1Origin of the coordinate system is along Z1Distance of the shaft.
S2.6: respectively calculating each rope traction point P of 6 ropes of the connecting tooli(i ═ 1,2,3,4,5,6) in O1-X1Y1Z1Coordinate (x ') in coordinate system'p1i,y′p1i,z′p1i) Obtained by the following formula:
Figure BDA0003221807870000131
Figure BDA0003221807870000132
Figure BDA0003221807870000133
wherein p represents a rope pulling point, 1 represents O1-X1Y1Z1The coordinate system established is the reference system, i represents the ith rope connecting the workpiece.
S2.7: respectively calculating each rope traction point P of 6 ropes connected with the circular tooli(i ═ 1,2,3,4,5,6) in O2-X2Y2Z2Coordinate (x ') in coordinate system'p2i,y′p2i,z′p2i) Obtained by the following formula:
Figure BDA0003221807870000134
Figure BDA0003221807870000135
D12converting the matrix for translation;
wherein p represents a rope pulling point, 2 represents O2-X2Y2Z2The coordinate system established is a reference system, i represents the ith rope connected with the tool.
S2.8: measuring the tension value F of 6 ropes through a tension sensor2i(i ═ 1,2,3,4,5,6), and the tension of each rope is resolved to O2-X2Y2Z2X of a coordinate system2Axis, Y2Axis, Z2On the shaft and respectively obtain F2ix,F2iy,F2izIt can be obtained by the following formula:
Figure BDA0003221807870000141
s2.9: center of mass M of circular tool and assembled objecteRelative to O2-X2Y2Z2The coordinates of the coordinate system are (x)me2,yme2,zme2) Gravity G of the whole body consisting of the tool and the assembled object1Decomposition to O2-X2Y2Z2X of a coordinate system2Axis, Y2Axis, Z2On the shaft to obtain G12x,G12y,G12zIt can be obtained by the following formula:
Figure BDA0003221807870000142
wherein m represents the mass center, e represents the whole of the circular tool and the assembled object, and 2 represents O2-X2Y2Z2The coordinate system established is the reference system.
S2.10: respectively establishing X2Axis, Y2Axis, Z2The moment balance equation of (a) can be obtained by the following formula:
Figure BDA0003221807870000143
s2.11: the integral mass center M of the tool and the assembled object can be obtained by solving the three-axis moment balance equation (26)eRelative to O2-X2Y2Z2Coordinates (x) of a coordinate systemme2,yme2,zme2)。
S3: calculating the mass center of the assembled object:
s3.1: calculate the mass center M of the round frocksRelative to O2-X2Y2Z2Coordinates (x) of a coordinate systemms2,yms2,zms2) It can be obtained by the following formula:
Figure BDA0003221807870000151
Figure BDA0003221807870000152
s3.2: setting mass center M of assembled objectpRelative to O2-X2Y2Z2The coordinates of the coordinate system are (x)mp2,ymp2,zmp2) Finding M by centroid theorempCoordinate (x) ofmp2,ymp2,zmp2) It can be obtained by the following formula:
Figure BDA0003221807870000153
wherein m represents the centroid, p represents the whole of the object to be assembled, and 2 represents O2-X2Y2Z2The coordinate system established is the reference system.

Claims (10)

1. A method for measuring the mass center of an object in a large-space rope drive assembly process is characterized by comprising the following steps:
s1: measuring the mass center of the tool:
s1.1: establishing a coordinate system O0-X0Y0Z0And a coordinate system O1-X1Y1Z1；
S1.2: the rope drives the rigging equipment and evenly is connected to circular frock through 6 ropes, utilizes the rope to drive the rigging equipment with X circular frock0Rotating the shaft by an angle alpha and keeping the shaft still; at this time, a rope exit point C between the rope drive rigging equipment and the ropeiRelative to O0-X0Y0Z0The coordinates of the coordinate system are (x)c0i,yc0i,zc0i) I is 1,2,3,4,5, 6; rope traction point P between circular tool and ropeiRelative to O0-X0Y0Z0The coordinates of the coordinate system are (x)p0i,yp0i,zp0i)；
S1.3: respectively calculating the tension of each rope in 6 ropes connected with the circular tool at the position O0-X0Y0Z0Direction vector T in coordinate system0iAnd in O1-X1Y1Z1Direction vector T in coordinate system1i；
S1.4: respectively calculating rope pulling points P of 6 ropes connected with the circular tooliAt O1-X1Y1Z1Coordinates (x) in a coordinate systemp1i,yp1i,zp1i)；
S1.5: respectively measuring the tension values F of 6 ropes through tension sensors1iAnd the tension of each rope is respectively decomposed into O1-X1Y1Z1X of a coordinate system1Axis, Y1Axis and Z1On the shaft and respectively obtain F1ix,F1iy,F1iz；
S1.6: center of mass M of circular toolsRelative to O1-X1Y1Z1The coordinates of the coordinate system are (x)ms1,yms1,zms1) Gravity G of the circular tool0Decomposition to O1-X1Y1Z1X of a coordinate system1Axis, Y1Axis and Z1On the shaft and get G01x,G01y,G01zIt can be obtained by the following formula:
Figure FDA0003221807860000011
wherein m represents the center of mass of the circular tool, s represents the whole tool, and 1 represents O1-X1Y1Z1The established coordinate system is a reference system;
s1.7: respectively establishing X1Axis, Y1Axis and Z1The moment balance equation of the shaft can be obtained by the following formula:
Figure FDA0003221807860000021
s1.8: the centroid M of the tool can be obtained by solving the triaxial moment balance equation in the step S1.7sRelative to O1-X1Y1Z1Coordinates (x) of a coordinate systemms1,yms1,zms1)；
S2: measuring the center of mass of the tool and the assembled object as a whole:
s2.1: establishing a coordinate system O2-X2Y2Z2；
S2.2: the rope drives the rigging equipment and evenly is connected to circular frock through 6 ropes, and the circular frock is connected and is assembled the object, utilizes the rope to drive the whole of rigging equipment with centre of a circle frock and assembled the object and constitute with X0Rotating the shaft by an angle alpha and keeping the shaft still; at this time, a rope exit point C between the rope drive rigging equipment and the ropeiRelative to O0-X0Y0Z0The coordinates of the coordinate system are (x)c0i,yc0i,zc0i) (ii) a Rope traction P between circular tool and ropeiRelative to O0-X0Y0Z0The coordinate of the coordinate system is (x'p0i,y′p0i,z′p0i)；
S2.3: respectively calculating the tension of each rope in 6 ropes of the connecting tool at O0-X0Y0Z0Direction vector T 'under coordinate system'0iIn O1-X1Y1Z1Direction vector T 'under coordinate system'1iAnd in O2-X2Y2Z2Direction vector T 'under coordinate system'2i；
S2.4: respectively calculating each rope traction point P of 6 ropes connected with the circular tooliAt O1-X1Y1Z1Coordinate (x ') in coordinate system'p1i,y′p1i,z′p1i) And in O2-X2Y2Z2Coordinate (x ') in coordinate system'p2i,y′p2i,z′p2i)；
S2.5: measuring the tension value F of 6 ropes through a tension sensor2iAnd the tension of each rope is respectively decomposed into O2-X2Y2Z2X of a coordinate system2Axis, Y2Axis, Z2On the shaft and respectively obtain F2ix,F2iy,F2iz；
S2.6: center of mass M of circular tool and assembled objecteRelative to O2-X2Y2Z2The coordinates of the coordinate system are (x)me2,yme2,zme2) Gravity G of the whole body consisting of the tool and the assembled object1Decomposition to O2-X2Y2Z2X of a coordinate system2Axis, Y2Axis, Z2On the shaft to obtain G12x,G12y,G12zIt can be obtained by the following formula:
Figure FDA0003221807860000031
wherein m represents the mass center, e represents the whole of the circular tool and the assembled object, and 2 represents O2-X2Y2Z2The established coordinate system is a reference system;
s2.7: respectively establishing X2Axis, Y2Axis, Z2The moment balance equation of (a) can be obtained by the following formula:
Figure FDA0003221807860000032
s2.8: the integral mass center M formed by the tool and the assembled object can be obtained by solving the triaxial moment balance equation in the step S2.7eRelative to O2-X2Y2Z2Coordinates (x) of a coordinate systemme2,yme2,zme2)；
S3: calculating the mass center of the assembled object:
s3.1: calculate the mass center M of the round frocksRelative to O2-X2Y2Z2Coordinates (x) of a coordinate systemms2,yms2,zms2) It can be obtained by the following formula:
Figure FDA0003221807860000033
Figure FDA0003221807860000034
s3.2: setting mass center M of assembled objectpRelative to O2-X2Y2Z2The coordinates of the coordinate system are (x)mp2,ymp2,zmp2) Finding M by centroid theorempCoordinate (x) ofmp2,ymp2,zmp2) It can be obtained by the following formula:
Figure FDA0003221807860000041
wherein m represents the centroid, p represents the whole of the object to be assembled, and 2 represents O2-X2Y2Z2The coordinate system established is the reference system.
2. The method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 1, is characterized in that: in S1.1, the oxygen atom0-X0Y0Z0The coordinate system is a world coordinate system of the assembly space of the rope drive assembly equipment;
the coordinate system O1-X1Y1Z1Is obtained by the following steps: establishing a space coordinate system by taking the center of the circular tool as an original point, and winding the space coordinate system in parallel by X0Obtaining a coordinate system O by rotating the shaft by an angle alpha1-X1Y1Z1。
3. The method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 2, is characterized in that: s1.3, the direction vector T0iObtained by the following formula:
Figure FDA0003221807860000042
Figure FDA0003221807860000043
wherein, c is the rope outlet point of the belt meter, p is the rope drawing point, 0 is O0-X0Y0Z0The established world coordinate is a reference system, and i represents the ith rope connected with the tool on the rope drive assembly equipment;
the direction vector T1iObtained by the following formula:
T0i＝R′x(α)T1i+D′01
Figure FDA0003221807860000044
Figure FDA0003221807860000045
D′01is a translation conversion matrix, R'x(α) is a rotation transformation matrix, x1,y1,z1Are each O1-X1Y1Z1Origin of coordinate system is O0-X0Y0Z0Coordinate values on the X, Y and Z axes in the coordinate system.
4. The method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 3, wherein the mass center of the object is measured by the following steps: s1.4, the rope pulling point Pi(i ═ 1,2,3,4,5,6) in O1-X1Y1Z1Coordinates (x) in a coordinate systemp1i,yp1i,zp1i) Obtained by the following formula:
Figure FDA0003221807860000051
Figure FDA0003221807860000052
Figure FDA0003221807860000053
D01for translating the transformation matrix, RxAnd (alpha) is a rotation transformation matrix.
5. The method for measuring the mass center of an object in the large-space rope-driven assembly process as claimed in claim 4, wherein the method is characterized in thatIn the following steps: s2.1, the coordinate system O2-X2Y2Z2Is obtained by the following steps: establishing a space coordinate system by taking any vertex or central point of the assembled object as an origin, wherein the coordinate values of the space coordinate system and a coordinate system O0-X0Y0Z0Equidirectional, space coordinate system surrounding X0Obtaining a coordinate system O by rotating the shaft by an angle alpha2-X2Y2Z2。
6. The method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 5, wherein the mass center of the object is measured by the following steps: in S2.3, the direction vector T'0iObtained by the following formula:
Figure FDA0003221807860000054
Figure FDA0003221807860000055
wherein, c is the rope outlet point of the belt meter, p is the rope drawing point, 0 is O0-X0Y0Z0The established world coordinate is a reference system, and i represents the ith rope of the rope drive assembly equipment connecting tool;
the direction vector T'1iObtained by the following formula:
T′0i＝R′x(α)T′1i+D′01
Figure FDA0003221807860000061
Figure FDA0003221807860000062
D′01for translating momentR 'of'x(α) is a translation and rotation transformation matrix;
the direction vector T'2iObtained by the following formula:
T′1i＝T′2i+D′12
Figure FDA0003221807860000063
D′12converting the matrix for translation; x is the number oflRepresents O2-X2Y2Z2The origin of the coordinate system is at O1-X1Y1Z1In the coordinate system at X1Coordinate value of axial direction, ylRepresents O2-X2Y2Z2The origin of the coordinate system is at O1-X1Y1Z1In the coordinate system at Y1Coordinate values in the axial direction, wherein h represents O2-X2Y2Z2Origin of coordinate system relative to O1-X1Y1Z1Origin of the coordinate system is along Z1Distance of the shaft.
7. The method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 6, wherein the mass center of the object is measured by the following steps: s2.4, the rope pulling point PiAt O1-X1Y1Z1Coordinate (x ') in coordinate system'p1i,y′p1i,z′p1i) Obtained by the following formula:
Figure FDA0003221807860000064
Figure FDA0003221807860000065
Figure FDA0003221807860000066
wherein p represents a rope pulling point, 1 represents O1-X1Y1Z1The coordinate system is established as a reference system, i represents the ith rope connected with the workpiece;
the rope traction point Pi(i ═ 1,2,3,4,5,6) in O2-X2Y2Z2Coordinate (x ') in coordinate system'p2i,y′p2i,z′p2i) Obtained by the following formula:
Figure FDA0003221807860000071
Figure FDA0003221807860000072
D12converting the matrix for translation; wherein p represents a rope pulling point, 2 represents O2-X2Y2Z2The coordinate system established is a reference system, i represents the ith rope connected with the tool.
8. The method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 7, is characterized in that: in S1.5, F1ix,F1iy,F1izObtained from the following equation:
Figure FDA0003221807860000073
9. the method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 8, wherein the mass center of the object is measured by the following steps: in S2.5, F2ix,F2iy,F2izObtained from the following equation:
Figure FDA0003221807860000074
10. the method for measuring the mass center of an object in the large-space rope drive assembly process according to claim 9, is characterized in that: the circular tool comprises a disc (1) and a connecting part (2), wherein 6 rope traction holes are uniformly formed in the disc (1), and the connecting part (2) is arranged on the disc (1) and used for connecting an assembled object.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102507091A (en) * 2011-11-22 2012-06-20 天津大学 Object mass center measuring device and method
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