WO2020138587A1 - Method for calculating maximum rectangular prism workspace of multi-axis machine - Google Patents

Method for calculating maximum rectangular prism workspace of multi-axis machine Download PDF

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WO2020138587A1
WO2020138587A1 PCT/KR2019/002551 KR2019002551W WO2020138587A1 WO 2020138587 A1 WO2020138587 A1 WO 2020138587A1 KR 2019002551 W KR2019002551 W KR 2019002551W WO 2020138587 A1 WO2020138587 A1 WO 2020138587A1
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angle prism
maximum
calculating
axis machine
end device
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PCT/KR2019/002551
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French (fr)
Korean (ko)
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양승한
이훈희
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경북대학교 산학협력단
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q15/00—Automatic control or regulation of feed movement, cutting velocity or position of tool or work
    • B23Q15/007—Automatic control or regulation of feed movement, cutting velocity or position of tool or work while the tool acts upon the workpiece
    • B23Q15/013—Control or regulation of feed movement
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]

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  • the present invention relates to a method for calculating a maximum right angle prism working space of a multi-axis machine, and more specifically, by calculating a right-angle prism having a maximum size reachable by an end device of a multi-axis machine, a working space in a design stage and a process preparation stage of a workpiece.
  • a method for calculating the maximum right angle prism working space of a multi-axis machine that provides a quantitative criterion for determining the arrangement of tables and structures so that it is possible to easily check the processability due to constraints and secure the maximum working space when designing a multi-axis machine. It is about.
  • Rectangular Prism work space refers to a work space composed of positions that can be reached by an end effector of a multi-axis machine in a rectangular coordinate system.
  • ISO230-6 stipulates to measure the right angle prism of the machine tool in order to evaluate the position performance of the machine tool.
  • a multi-axis machine made of a serial mechanism can intuitively grasp the right-angle prism working space.
  • the parallel mechanism has an advantage in that a moving mass is distributed to each actuator to enable agile driving and to take a flexible tool posture.
  • the multi-axis machine including such a parallel mechanism has a non-linear working space in its shape due to mechanical restraint, and therefore cannot present an intuitive working space.
  • the present invention has been proposed to solve the above problems, and aims to calculate a work space of a right-angled prism shape of a maximum size reachable by a terminal device of a multi-axis machine through a mathematical operation without physical confirmation.
  • the present invention in a method for calculating the maximum working space of a cuboid shape workable in a multi-axis machine
  • It provides a method of calculating a maximum right angle prism working space of a multi-axis machine, including; a right angle prism included in the limiting right angle prism, calculating a right angle prism having a maximum size that can be reached by the end device.
  • the present invention is characterized in that the step of calculating the reachable position of the end device is to calculate the reachable position of the end device by calculating the kinematics of the multi-axis machine by combining the possible feed distance and rotation angle of each drive shaft of the multi-axis machine. .
  • the divided volume of the space division step of the present invention is characterized in that the shape of a rectangular parallelepiped.
  • the reachability determination step of the present invention includes a transfer distance and a rotation angle of each drive shaft for the end device calculated by inverse kinematics calculation for the multi-axis machine to be located at each vertex of the divided volume. It is characterized by being determined according to whether or not.
  • a terminal device is reached in the step of determining whether it is reachable among the vertices constituting the intermediate-level right-angle prism by forming a right-angled prism in which the divided volumes are combined into a cuboid shape It is characterized in that the intermediate step right angle prism is extended so that the vertex determined to be impossible is not included.
  • the step of calculating the maximum right angle prism of the present invention is characterized in that the right angle prism of the maximum size reachable by the end device is calculated while extending the intermediate step right angle prism to the limit right angle prism.
  • the step of calculating the maximum right angle prism of the present invention is characterized by reducing the calculation time by forming the intermediate step right angle prism by reflecting the symmetry condition of the multi-axis machine drive shaft.
  • the step of calculating the maximum right-angle prism of the present invention is characterized by reducing the calculation time by forming the intermediate-stage right-angle prism by reflecting the position of the workpiece table of the multi-axis machine.
  • the method for calculating the maximum right-angle prism work space of a multi-axis machine according to the present invention has an effect of easily determining whether a process is possible due to a work space limitation in a design step and a process preparation step of a workpiece.
  • the present invention has an effect of providing a quantitative criterion for determining the arrangement of tables and structures so as to secure a maximum working space when designing a multi-axis machine.
  • the present invention has an effect of providing a reference space for performance evaluation in process design of a multi-axis machine.
  • 1 is a view showing a maximum right-angle prism showing a working space of a multi-axis machine.
  • FIG. 2 is a perspective view of a parallel mechanism processing machine of Exechon.
  • 3 is a view showing the degree of freedom and coordinate system for the parallel mechanism processing machine of Exechon.
  • FIG. 4 is a flowchart of a method for calculating a maximum right-angle prism working space according to the present invention.
  • FIG. 5 is a view showing the reachable position of the PKM end device calculated by the end device reachable position calculating step of the present invention.
  • FIG. 6 is a detailed flowchart of the reachability determination step according to the present invention.
  • first may be referred to as a second component without departing from the scope of rights described in this document, and similarly, the second component may be referred to as a first component.
  • 1 is a view showing a maximum right-angle prism showing a working space of a multi-axis machine.
  • the end device of a multi-axis machine can be reached at any position inside the maximum right angle prism. Therefore, machining is not possible when the area to be processed is outside the maximum right angle prism of the multi-axis machine. Therefore, the maximum right angle prism of a multi-axis machine must be defined and presented in advance to determine whether the multi-axis machine can work.
  • FIG. 2 is a perspective view of an Exechon parallel mechanism processing machine
  • FIG. 3 is a view showing a degree of freedom and a coordinate system for the Exechon parallel mechanism processing machine.
  • PKM has been successfully commercialized among parallel and hybrid machine tools, and Neumann developed a structure to replace the ball joint in the Tricept structure to secure sufficient rigidity and precision for processing. In addition, since there are all degrees of freedom for relative motion on the tool side, it is used for processing large parts such as aircraft wings in connection with an expansion axis such as a gantry system.
  • Exechon's parallel mechanism processing machine 100 forms a hybrid structure in which a 3-axis parallel mechanism and a 2-axis series mechanism are combined.
  • the 5-axis parallel mechanism includes a base frame 110, a moving frame 120, a first link 130, a second link 140, a third link 150, a fourth link 160, and a fifth link 170 ).
  • the base frame 110 maintains a stationary state and forms the body 210 of the 5-axis parallel mechanism.
  • the moving frame 120 is disposed spaced apart from the base frame 110 at a predetermined interval, and is movable relative to the base frame 110.
  • the first link 130, the second link 140, and the third link 150 are slidable through one end of the base frame 110, and the other end is fixed to the moving frame 120.
  • Linear actuators of the first to third links 150 may be employed, and the first to third links 150 may be formed to have different lengths, respectively.
  • the first to third links 150 having the other end fixed to the moving frame form a three-axis parallel mechanism.
  • One end of the fourth link 160 is hinged to the moving frame 120.
  • the fifth link 170 is hinged to one end of the fourth link 160 and a tool is coupled to the other end. That is, the fifth link 170 corresponds to the spindle.
  • the fourth link 160 and the fifth link 170 form a two-axis serial mechanism.
  • the parallel mechanism processing machine 100 of Exechon is connected to a 2-axis serial mechanism to a 3-axis parallel mechanism.
  • PKM adopts a hybrid method in which a series mechanism and a parallel mechanism are combined, so it is difficult to intuitively define the maximum right-angle prism working space.
  • FIG. 4 is a flowchart of a method for calculating a maximum right-angle prism work space according to the present invention
  • FIG. 5 is a view showing the reachable position of the PKM end device calculated by the end device reachable position calculating step (S10) of the present invention
  • 6 is a detailed flowchart of the reachability determination step S40 according to the present invention.
  • the method for calculating the maximum right-angle prism working space of the multi-axis machine is an end device reachable position calculation step (S10), a limit right-angle prism calculation step (S20), a space division step (S30), and a reachability determination step (S40). , Maximum right-angle prism calculation step (S50).
  • the maximum square prism working space of a multi-axis machine refers to the maximum working space of a rectangular parallelepiped shape that can work on a multi-axis machine.
  • the end device reachable position calculation step S10 is a step of calculating a position coordinate reachable by the end device of the multi-axis machine.
  • the reachable position of the end device is calculated by the forward kinematic calculation of the multi-axis machine by combining the possible feed distance and rotation angle of each drive shaft of the multi-axis machine.
  • the calculation of the forward kinematics means calculating the coordinates of the end device for the moving conditions of each drive shaft.
  • the region where the end device of the PKM can be reached has a non-linear shape such as a shape of a ship sailing the sea, not a cuboid.
  • the method for calculating a maximum right-angle prism working space according to the present invention is to derive a right-angle prism having a maximum size that can be included in a region reachable by the end device as shown in FIG. 5.
  • the marginal right angle prism calculation step (S20) is a step of defining a calculation limit for the right angle prism to be calculated.
  • the limiting right angle prism is defined by the maximum and minimum values in the x-axis direction of the end device reachable position, the maximum and minimum values in the y-axis direction, and the maximum and minimum values in the z-axis direction.
  • the marginal right angle prism also includes a region where the end device of a multi-axis machine is unreachable. Therefore, it is not necessary to examine the space above the limiting right-angle prism in calculating the maximum right-angle prism working space.
  • the marginal right angle prism can be expressed by the following equation.
  • V TEMP Is the marginal right-angle prism area
  • x max Is the maximum value in the x-axis direction of the end device reachable position
  • x min Is the minimum value in the x-axis direction of the end device reachable position
  • y max Is the maximum value in the y-axis direction of the end device reachable position
  • y min Is the minimum value in the y-axis direction of the reachable end device
  • z max Is the maximum value in the z-axis direction of the end device reachable position
  • z min is the minimum value in the z-axis direction of the end device reachable position.
  • the location of the worktable is determined, it can be defined as ZWorktable instead of Zmin value.
  • the space division step (S30) is a step of dividing the marginal right angle prism into a plurality of divided volumes.
  • the size of the divided volume can be appropriately selected in consideration of the computing power of the computer.
  • the reachability determining step S40 is a step of determining whether each vertex of the divided volume divided in the space dividing step S30 is reachable by the end device.
  • the transport distance and rotation angle of each drive shaft to be located at each vertex of the divided volume are determined according to whether the drive shaft is included in the implementable region.
  • each drive shaft to be located at each vertex of the divided volume are obtained by inverse kinematic calculations for a multi-axis machine.
  • the inverse kinematic calculation refers to calculating the moving distance and rotation angle of each drive shaft to realize a given position of the multi-axis machine end device.
  • each vertex of the divided volume is determined whether the end device of the multi-axis machine is reachable or unreachable.
  • the maximum right-angle prism calculating step S50 is a right-angle prism included in the limit right-angle prism, and is a step of calculating a right-angle prism having a maximum size reachable by the terminal device.
  • a right-angle prism in an intermediate step in which the divided volume is combined into a rectangular parallelepiped shape is formed.
  • the intermediate step right angle prism is gradually expanded so that the vertex determined by the end device to be unreachable is not included in the step S40 of determining whether it is reachable.
  • the right angle prism of the maximum size reachable by the end device is calculated while the intermediate right angle prism is extended to the limit right angle prism.
  • the calculation time can be reduced by forming the intermediate-level right-angle prism by reflecting the symmetry condition of the multi-axis machine drive shaft.
  • the calculation time can be reduced by forming the intermediate-level right-angle prism by reflecting the position of the workpiece table of the multi-axis machine.
  • the calculation time can be reduced by excluding an area lower than the work table position from the calculation.
  • the method for calculating the maximum right-angle prism working space of a multi-axis machine calculates the right-angle prism of the largest size reachable by the end device of the multi-axis machine, thereby enabling processability due to work space limitations in the design stage and process preparation stage of the workpiece. At the same time, it has the effect of providing a quantitative criterion for determining the arrangement of tables and structures so as to ensure the maximum working space when designing a multi-axis machine.

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Abstract

Disclosed is a method for calculating a maximum rectangular prism workspace of a multi-axis machine. The disclosed method for calculating a maximum rectangular prism workspace of a multi-axis machine comprises: an end effector-reachable position calculation step (S10) for calculating the coordinates of a position reachable by an end effector of the multi-axis machine; a limit rectangular prism calculation step (S20) for calculating a limit rectangular prism defined by the x-axis maximum and minimum values, the y-axis maximum and minimum values, and the z-axis maximum and minimum values of the position reachable by the end effector; a space division step (S30) for dividing the limit rectangular prism into multiple divided volumes; a reachability determination step (S40) for determining whether the end effector can reach the respective vertexes of the divided volumes; and a maximum rectangular prism calculation step (S50) for calculating a rectangular prism which has the maximum size reachable by the end effector among rectangular prisms included in the limit rectangular prism.

Description

다축기계의 최대직각프리즘 작업공간 산출방법How to calculate the maximum right angle prism working space of a multi-axis machine
본 발명은 다축기계의 최대직각프리즘 작업공간 산출방법에 관한 것으로서, 더욱 상세하게는 다축기계의 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출함으로써, 가공품의 설계단계 및 공정준비단계에서 작업 공간 제약으로 인한 공정가능여부를 쉽게 확인할 수 있는 동시에, 다축기계 설계 시에 최대한의 작업공간을 확보할 수 있도록 테이블 및 구조물의 배치를 결정하는 정량적 기준을 제공하는 다축기계의 최대직각프리즘 작업공간 산출방법에 관한 것이다.The present invention relates to a method for calculating a maximum right angle prism working space of a multi-axis machine, and more specifically, by calculating a right-angle prism having a maximum size reachable by an end device of a multi-axis machine, a working space in a design stage and a process preparation stage of a workpiece. A method for calculating the maximum right angle prism working space of a multi-axis machine that provides a quantitative criterion for determining the arrangement of tables and structures so that it is possible to easily check the processability due to constraints and secure the maximum working space when designing a multi-axis machine. It is about.
직각 프리즘(Rectangular Prism) 작업공간은 직교좌표계에서 다축기계의 말단장치(End effector)가 도달할 수 있는 위치들로 이뤄진 작업공간을 말한다.Rectangular Prism work space refers to a work space composed of positions that can be reached by an end effector of a multi-axis machine in a rectangular coordinate system.
통상적으로 CAD/CAM 작업은 직교좌표계에서 수행되기 때문에, 해당 다축기계로 소정 작업의 가능여부를 판단하기 위해서는 다축기계의 직각프리즘 작업공간이 명확히 제시되어야 한다.Since the CAD/CAM work is usually performed in the Cartesian coordinate system, the right-angle prism work space of the multi-axis machine must be clearly presented in order to determine whether a given work is possible with the multi-axis machine.
이에 따라 ISO230-6에서는 공작기계의 위치 성능을 평가하기 위해서 해당 공직기계의 직각프리즘을 측정하도록 규정하고 있다.Accordingly, ISO230-6 stipulates to measure the right angle prism of the machine tool in order to evaluate the position performance of the machine tool.
직렬기구로 이뤄진 다축기계는 직각프리즘 작업공간을 직관적으로 쉽게 파악이 가능하다.A multi-axis machine made of a serial mechanism can intuitively grasp the right-angle prism working space.
한편, 로봇, 공작기계와 같이 다축 가공기계의 활용분야가 다양해지면서, 일반적인 직렬형태의 구조가 아닌 병렬 또는 직렬/병렬 하이브리드 구조의 메커니즘을 채택한 기계가 개발되고 있으며, 일부 구조는 가공용으로 출시되고 있다.On the other hand, as the application fields of multi-axis processing machines such as robots and machine tools are diversified, machines employing parallel or serial/parallel hybrid structures rather than general serial structures are being developed, and some structures are released for processing. .
병렬 메커니즘은 이동질량(Moving mass)이 각 액추에이터에 분산되어 민첩한 구동이 가능하고, 유연한 공구 자세를 취할 수 있는 장점이 있다.The parallel mechanism has an advantage in that a moving mass is distributed to each actuator to enable agile driving and to take a flexible tool posture.
이러한 병렬기구가 포함된 다축기계는 기구적 구속으로 인해 그 형상이 비선형적 작업공간을 보이고 있어, 직관적인 작업공간을 제시할 수 없다.The multi-axis machine including such a parallel mechanism has a non-linear working space in its shape due to mechanical restraint, and therefore cannot present an intuitive working space.
이로 인해 소정 작업을 수행하기 전에 또는 수행 중에 작업경로에 대한 검사가 요구된다. 이는 매우 번거롭고 시간이 많이 소요되어 생산성을 떨어뜨리는 요인이 되고 있다.For this reason, it is required to inspect the work path before or during a predetermined operation. This is very cumbersome and time-consuming, which is a factor that decreases productivity.
따라서 병렬기구가 포함된 다축기계의 최대직각프리즘 작업공간을 산출할 수 있는 효과적인 방법의 개발이 절실히 요청된다.Therefore, the development of an effective method for calculating the maximum right angle prism working space of a multi-axis machine including a parallel mechanism is urgently required.
본 발명은 상기와 같은 문제를 해결하고자 제안된 것으로, 물리적 확인 없이 수학적 연산을 통해서 다축기계의 말단장치에 의해 도달가능한 최대 크기의 직각프리즘 형상의 작업공간을 산출하는 것을 목적으로 한다.The present invention has been proposed to solve the above problems, and aims to calculate a work space of a right-angled prism shape of a maximum size reachable by a terminal device of a multi-axis machine through a mathematical operation without physical confirmation.
본 발명은 다축기계에서 작업가능한 직육면체 형상의 최대작업공간을 산출하는 방법에 있어서, The present invention in a method for calculating the maximum working space of a cuboid shape workable in a multi-axis machine,
다축기계의 말단장치가 도달가능한 위치좌표를 산출하는 말단장치 도달가능위치 산출단계;An end device reachable position calculating step of calculating a position coordinate reachable by the end device of the multi-axis machine;
상기 말단장치 도달가능위치의 x축방향의 최대치와 최소치, y 축방향의 최대치와 최소치, z 축방향의 최대치와 최소치에 의해 정의되는 한계직각프리즘을 산출하는 한계직각프리즘 산출단계;A limiting right angle prism calculation step of calculating a limiting right angle prism defined by a maximum value and a minimum value in the x-axis direction, a maximum value and a minimum value in the y-axis direction, and a maximum value and a minimum value in the z-axis direction of the reachable position of the end device;
상기 한계직각프리즘을 복수의 분할체적으로 분할하는 공간분할단계;A space division step of dividing the marginal right angle prism into a plurality of divided volumes;
상기 분할체적의 각 꼭지점이 상기 말단장치에 의해 도달가능한지 여부를 판단하는 도달가능여부 판단단계;A reachability determining step of determining whether each vertex of the divided volume is reachable by the end device;
상기 한계직각프리즘에 포함되는 직각프리즘으로서, 상기 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출하는 최대직각프리즘 산출단계;를 포함하는, 다축기계의 최대직각프리즘 작업공간 산출방법을 제공한다.It provides a method of calculating a maximum right angle prism working space of a multi-axis machine, including; a right angle prism included in the limiting right angle prism, calculating a right angle prism having a maximum size that can be reached by the end device.
또한 본 발명은 상기 말단장치 도달가능위치 산출단계는 다축기계 각 구동축의 가능한 이송거리와 회전각도를 조합하여 상기 다축기계에 대한 정기구학 계산에 의해 말단장치의 도달가능위치를 산출하는 것을 특징으로 한다.In addition, the present invention is characterized in that the step of calculating the reachable position of the end device is to calculate the reachable position of the end device by calculating the kinematics of the multi-axis machine by combining the possible feed distance and rotation angle of each drive shaft of the multi-axis machine. .
또한 본 발명의 상기 공간분할단계의 분할체적은 직육면체 형상인 것을 특징으로 한다.In addition, the divided volume of the space division step of the present invention is characterized in that the shape of a rectangular parallelepiped.
또한 본 발명의 상기 도달가능여부 판단단계는 상기 다축기계에 대한 역기구학 계산에 의해 계산된 말단장치가 상기 분할체적의 각 꼭지점에 위치하기 위한 각 구동축의 이송거리와 회전각도가 구현가능한 영역에 포함되는지 여부에 따라 결정되는 것을 특징으로 한다.In addition, the reachability determination step of the present invention includes a transfer distance and a rotation angle of each drive shaft for the end device calculated by inverse kinematics calculation for the multi-axis machine to be located at each vertex of the divided volume. It is characterized by being determined according to whether or not.
또한 본 발명의 상기 최대직각프리즘 산출단계는 상기 분할체적을 직육면체 형상으로 조합한 중간단계의 직각프리즘을 형성하고, 상기 중간단계 직각프리즘을 구성하는 꼭지점 중에 상기 도달가능여부 판단단계에서 말단장치가 도달불가능한 것으로 판단된 꼭지점이 포함되지 않도록 중간단계 직각프리즘을 확장시키는 것을 특징으로 한다.In addition, in the step of calculating the maximum right-angle prism of the present invention, a terminal device is reached in the step of determining whether it is reachable among the vertices constituting the intermediate-level right-angle prism by forming a right-angled prism in which the divided volumes are combined into a cuboid shape It is characterized in that the intermediate step right angle prism is extended so that the vertex determined to be impossible is not included.
또한 본 발명의 상기 최대직각프리즘 산출단계는 상기 중간단계 직각프리즘을 한계직각프리즘까지 확장시키면서 상기 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출하는 것을 특징으로 한다.In addition, the step of calculating the maximum right angle prism of the present invention is characterized in that the right angle prism of the maximum size reachable by the end device is calculated while extending the intermediate step right angle prism to the limit right angle prism.
또한 본 발명의 상기 최대직각프리즘 산출단계는 상기 다축기계 구동축의 대칭조건을 반영하여 상기 중간단계 직각프리즘을 형성함으로써 계산시간을 줄이는 것을 특징으로 한다.In addition, the step of calculating the maximum right angle prism of the present invention is characterized by reducing the calculation time by forming the intermediate step right angle prism by reflecting the symmetry condition of the multi-axis machine drive shaft.
또한 본 발명의 상기 최대직각프리즘 산출단계는 상기 다축기계의 공작물 테이블 위치를 반영하여 상기 중간단계 직각프리즘을 형성함으로써 계산시간을 줄이는 것을 특징으로 한다.In addition, the step of calculating the maximum right-angle prism of the present invention is characterized by reducing the calculation time by forming the intermediate-stage right-angle prism by reflecting the position of the workpiece table of the multi-axis machine.
본 발명에 따른 다축기계의 최대직각프리즘 작업공간 산출방법은 가공품의 설계단계 및 공정준비단계에서 작업공간 제약으로 인한 공정가능여부를 쉽게 파악할 수 있는 효과가 있다.The method for calculating the maximum right-angle prism work space of a multi-axis machine according to the present invention has an effect of easily determining whether a process is possible due to a work space limitation in a design step and a process preparation step of a workpiece.
또한 본 발명은 다축기계 설계 시에 최대한의 작업공간을 확보 할 수 있도록 테이블 및 구조물의 배치를 결정하는 정량적 기준을 제공하는 효과가 있다.In addition, the present invention has an effect of providing a quantitative criterion for determining the arrangement of tables and structures so as to secure a maximum working space when designing a multi-axis machine.
또한 본 발명은 다축기계의 공정설계시 성능평가의 기준공간을 제공하는 효과가 있다.In addition, the present invention has an effect of providing a reference space for performance evaluation in process design of a multi-axis machine.
상술한 효과와 더불어 본 발명의 구체적인 효과는 이하 발명을 실시하기 위한 구체적인 사항을 설명하면서 함께 기술한다.In addition to the above-described effects, the concrete effects of the present invention will be described together while describing the specific matters for carrying out the present invention.
도 1은 다축기계의 작업공간을 나타내는 최대직각프리즘을 도시한 도면이다.1 is a view showing a maximum right-angle prism showing a working space of a multi-axis machine.
도 2는 Exechon사의 병렬기구 가공기계의 사시도이다.2 is a perspective view of a parallel mechanism processing machine of Exechon.
도 3은 Exechon사의 병렬기구 가공기계에 대한 자유도와 좌표계를 도시한 도면이다.3 is a view showing the degree of freedom and coordinate system for the parallel mechanism processing machine of Exechon.
도 4는 본 발명에 따른 최대직각프리즘 작업공간 산출방법에 대한 흐름도이다.4 is a flowchart of a method for calculating a maximum right-angle prism working space according to the present invention.
도 5는 본 발명의 말단장치 도달가능위치 산출단계에 의해 산출된 PKM 말단장치의 도달가능위치를 도시한 도면이다.5 is a view showing the reachable position of the PKM end device calculated by the end device reachable position calculating step of the present invention.
도 6은 본 발명에 따른 도달가능여부 판단단계의 상세 흐름도이다.6 is a detailed flowchart of the reachability determination step according to the present invention.
이하, 본 문서의 다양한 실시예가 첨부된 도면을 참조하여 기재된다. 그러나 이는 본 문서에 기재된 기술을 특정한 실시 형태에 대해 한정하려는 것이 아니며, 본 문서의 실시예의 다양한 변경(modifications), 균등물(equivalents), 및/또는 대체물(alternatives)을 포함하는 것으로 이해되어야 한다. 도면의 설명과 관련하여, 유사한 구성요소에 대해서는 유사한 참조 부호가 사용될 수 있다.Hereinafter, various embodiments of this document will be described with reference to the accompanying drawings. However, this is not intended to limit the techniques described in this document to specific embodiments, and it should be understood that it includes various modifications, equivalents, and/or alternatives of embodiments of the document. In connection with the description of the drawings, similar reference numerals may be used for similar elements.
또한, 본 문서에서 사용된 "제1," "제2," 등의 표현들은 다양한 구성요소들을, 순서 및/또는 중요도에 상관없이 수식할 수 있고, 한 구성요소를 다른 구성요소와 구분하기 위해 사용될 뿐 해당 구성요소들을 한정하지 않는다. 예를 들면, '제1 부분'과 '제2 부분'은 순서 또는 중요도와 무관하게, 서로 다른 부분을 나타낼 수 있다. 예를 들면, 본 문서에 기재된 권리 범위를 벗어나지 않으면서 제1 구성요소는 제2 구성요소로 명명될 수 있고, 유사하게 제2 구성요소도 제1 구성요소로 바꾸어 명명될 수 있다.In addition, expressions such as "first," "second," and the like used in this document may modify various components, regardless of order and/or importance, to distinguish one component from another component. It is used but does not limit the components. For example, the'first part' and the'second part' may indicate different parts regardless of order or importance. For example, the first component may be referred to as a second component without departing from the scope of rights described in this document, and similarly, the second component may be referred to as a first component.
또한, 본 문서에서 사용된 용어들은 단지 특정한 실시예를 설명하기 위해 사용된 것으로, 다른 실시예의 범위를 한정하려는 의도가 아닐 수 있다. 단수의 표현은 문맥상 명백하게 다르게 뜻하지 않는 한, 복수의 표현을 포함할 수 있다. 기술적이거나 과학적인 용어를 포함해서 여기서 사용되는 용어들은 본 문서에 기재된 기술 분야에서 통상의 지식을 가진 자에 의해 일반적으로 이해되는 것과 동일한 의미를 가질 수 있다. 본 문서에 사용된 용어들 중 일반적인 사전에 정의된 용어들은, 관련 기술의 문맥상 가지는 의미와 동일 또는 유사한 의미로 해석될 수 있으며, 본 문서에서 명백하게 정의되지 않는 한, 이상적이거나 과도하게 형식적인 의미로 해석되지 않는다. 경우에 따라서, 본 문서에서 정의된 용어일지라도 본 문서의 실시예들을 배제하도록 해석될 수 없다.Also, the terms used in this document are only used to describe specific embodiments, and may not be intended to limit the scope of other embodiments. Singular expressions may include plural expressions, unless the context clearly indicates otherwise. Terms used herein, including technical or scientific terms, may have the same meaning as commonly understood by a person skilled in the art described in this document. Among the terms used in this document, terms defined in the general dictionary may be interpreted as having the same or similar meaning in the context of the related art, and are ideally or excessively formal, unless explicitly defined in this document. Is not interpreted as In some cases, even terms defined in this document cannot be interpreted to exclude embodiments of the document.
도 1은 다축기계의 작업공간을 나타내는 최대직각프리즘을 도시한 도면이다.1 is a view showing a maximum right-angle prism showing a working space of a multi-axis machine.
도 1을 참조하여 설명한다.This will be described with reference to FIG. 1.
다축기계의 말단장치는 최대직각프리즘 내부 어느 위치에나 도달가능하다. 따라서 가공하고자 하는 영역이 다축기계의 최대직각프리즘을 벗어나는 경우에는 가공이 불가능하다. 따라서 다축기계의 최대직각프리즘이 사전에 정의되어 제시되어야 당해 다축기계로 작업이 가능한지 여부를 판단할 수 있다.The end device of a multi-axis machine can be reached at any position inside the maximum right angle prism. Therefore, machining is not possible when the area to be processed is outside the maximum right angle prism of the multi-axis machine. Therefore, the maximum right angle prism of a multi-axis machine must be defined and presented in advance to determine whether the multi-axis machine can work.
최대직각프리즘 작업공간을 직관적으로 파악하기 어려운 병렬기구가 구비된 다축기계에 대해 본 발명에 따른 작업공간 산출방법을 적용하고자 한다.It is intended to apply a work space calculation method according to the present invention to a multi-axis machine equipped with a parallel mechanism that is difficult to intuitively grasp the maximum right prism work space.
이를 위해 Exechon사의 병렬기구 가공기계(The parallel kinematic machine, 이하 PKM 이라 한다.)에 본 발명에 따른 작업공간 산출방법을 적용하였다.To this end, a method for calculating a work space according to the present invention was applied to the parallel kinematic machine (hereinafter referred to as PKM) of Exechon.
도 2는 Exechon사의 병렬기구 가공기계의 사시도이고, 도 3은 Exechon사의 병렬기구 가공기계에 대한 자유도와 좌표계를 도시한 도면이다.FIG. 2 is a perspective view of an Exechon parallel mechanism processing machine, and FIG. 3 is a view showing a degree of freedom and a coordinate system for the Exechon parallel mechanism processing machine.
PKM은 병렬, 하이브리드 공작기계 중 성공적으로 상용화된 형태로, Neumann이 Tricept 구조에서 볼 조인트를 대체하는 구조를 개발하여 가공에 충분한 강성과 정밀도를 확보하였다. 또한, 공구측에 상대 운동에 대한 자유도가 모두 있기 때문에, 갠트리 시스템 등의 확장 축과 연계하여 항공기 날개와 같은 대형 부품 가공에도 활용되고 있다.PKM has been successfully commercialized among parallel and hybrid machine tools, and Neumann developed a structure to replace the ball joint in the Tricept structure to secure sufficient rigidity and precision for processing. In addition, since there are all degrees of freedom for relative motion on the tool side, it is used for processing large parts such as aircraft wings in connection with an expansion axis such as a gantry system.
Exechon사의 병렬기구 가공기계(100)의 구조에 대해 간단히 설명한다.The structure of Exechon's parallel mechanism processing machine 100 will be briefly described.
Exechon사의 병렬기구 가공기계(100)는 3축 병렬기구와 2축 직렬기구가 조합된 하이브리드 구조를 이루고 있다.Exechon's parallel mechanism processing machine 100 forms a hybrid structure in which a 3-axis parallel mechanism and a 2-axis series mechanism are combined.
5축 병렬기구는 베이스 프레임(110), 이동 프레임(120), 제1 링크(130), 제2 링크(140), 제3 링크(150), 제4 링크(160), 제5 링크(170)를 포함한다.The 5-axis parallel mechanism includes a base frame 110, a moving frame 120, a first link 130, a second link 140, a third link 150, a fourth link 160, and a fifth link 170 ).
베이스 프레임(110)은 정지 상태를 유지하며, 5 축 병렬기구의 몸체(210)부를 형성한다.The base frame 110 maintains a stationary state and forms the body 210 of the 5-axis parallel mechanism.
이동 프레임(120)은 상기 베이스 프레임(110)에 소정 간격 이격되어 배치되며, 상기 베이스 프레임(110)에 대하여 이동이 가능하다.The moving frame 120 is disposed spaced apart from the base frame 110 at a predetermined interval, and is movable relative to the base frame 110.
제1 링크(130), 제2 링크(140), 제3 링크(150)는 일단이 상기 베이스 프레임(110)을 관통하여 슬라이딩 가능하며, 타단은 상기 이동 프레임(120)에 고정된다.The first link 130, the second link 140, and the third link 150 are slidable through one end of the base frame 110, and the other end is fixed to the moving frame 120.
제1 내지 제3 링크(150)는 리니어 액츄에이터가 채택될 수 있으며, 제1 내지 제3 링크(150)는 각각 상이한 길이로 형성될 수 있다. 결과적으로, 이동프레임에 타단이 고정된 제1 내지 제3 링크(150)는 3 축 병렬기구를 형성한다.Linear actuators of the first to third links 150 may be employed, and the first to third links 150 may be formed to have different lengths, respectively. As a result, the first to third links 150 having the other end fixed to the moving frame form a three-axis parallel mechanism.
제4 링크(160)는 일단은 상기 이동 프레임(120)에 힌지결합된다.One end of the fourth link 160 is hinged to the moving frame 120.
제5 링크(170)는 일단은 상기 제4 링크(160)에 힌지결합되며, 타단에는 공구가 결합된다. 즉, 제5 링크(170)는 스핀들에 해당된다.The fifth link 170 is hinged to one end of the fourth link 160 and a tool is coupled to the other end. That is, the fifth link 170 corresponds to the spindle.
제4 링크(160) 및 제5 링크(170)는 2축 직렬기구를 형성한다.The fourth link 160 and the fifth link 170 form a two-axis serial mechanism.
이와 같이 Exechon사의 병렬기구 가공기계(100)는 3축 병렬기구에 2축 직렬기구가 연결되어 있다.In this way, the parallel mechanism processing machine 100 of Exechon is connected to a 2-axis serial mechanism to a 3-axis parallel mechanism.
PKM은 직렬기구와 병렬기구가 조합된 하이브리드 방식을 취하고 있어, 직관적으로 최대직각프리즘 작업공간을 정의하기 어렵다.PKM adopts a hybrid method in which a series mechanism and a parallel mechanism are combined, so it is difficult to intuitively define the maximum right-angle prism working space.
도 4는 본 발명에 따른 최대직각프리즘 작업공간 산출방법에 대한 흐름도이고, 도 5는 본 발명의 말단장치 도달가능위치 산출단계(S10)에 의해 산출된 PKM 말단장치의 도달가능위치를 도시한 도면이고, 도 6은 본 발명에 따른 도달가능여부 판단단계(S40)의 상세 흐름도이다.4 is a flowchart of a method for calculating a maximum right-angle prism work space according to the present invention, and FIG. 5 is a view showing the reachable position of the PKM end device calculated by the end device reachable position calculating step (S10) of the present invention. 6 is a detailed flowchart of the reachability determination step S40 according to the present invention.
도 4 내지 도 6을 참조하여 설명한다.This will be described with reference to FIGS. 4 to 6.
본 발명에 따른 다축기계의 최대직각프리즘 작업공간 산출방법은 말단장치 도달가능위치 산출단계(S10), 한계직각프리즘 산출단계(S20), 공간분할단계(S30), 도달가능여부 판단단계(S40), 최대직각프리즘 산출단계(S50)를 포함한다.The method for calculating the maximum right-angle prism working space of the multi-axis machine according to the present invention is an end device reachable position calculation step (S10), a limit right-angle prism calculation step (S20), a space division step (S30), and a reachability determination step (S40). , Maximum right-angle prism calculation step (S50).
다축기계의 최대직각프리즘 작업공간이란 다축기계에서 작업가능한 직육면체 형상의 최대작업공간을 말한다.The maximum square prism working space of a multi-axis machine refers to the maximum working space of a rectangular parallelepiped shape that can work on a multi-axis machine.
말단장치 도달가능위치 산출단계(S10)는 다축기계의 말단장치가 도달가능한 위치좌표를 산출하는 단계이다.The end device reachable position calculation step S10 is a step of calculating a position coordinate reachable by the end device of the multi-axis machine.
이 단계에서는 다축기계 각 구동축의 가능한 이송거리와 회전각도를 조합하여 상기 다축기계에 대한 정기구학 계산에 의해 말단장치의 도달가능위치를 산출한다.In this step, the reachable position of the end device is calculated by the forward kinematic calculation of the multi-axis machine by combining the possible feed distance and rotation angle of each drive shaft of the multi-axis machine.
여기서 정기구학 계산이란 각 구동축의 이동조건에 대해서 말단장치의 좌표를 산출하는 것을 말한다.Here, the calculation of the forward kinematics means calculating the coordinates of the end device for the moving conditions of each drive shaft.
도 5에 도시된 바와 같이, PKM의 말단장치가 도달가능한 영역은 직육면체가 아니라 바다를 항해하는 배 형상과 같은 비선형적 형상을 이루고 있다.As illustrated in FIG. 5, the region where the end device of the PKM can be reached has a non-linear shape such as a shape of a ship sailing the sea, not a cuboid.
본 발명에 의한 최대직각프리즘 작업공간 산출방법은 도 5와 같은 말단장치가 도달가능한 영역에 포함될 수 있는 최대크기의 직각프리즘을 도출하는 것이다.The method for calculating a maximum right-angle prism working space according to the present invention is to derive a right-angle prism having a maximum size that can be included in a region reachable by the end device as shown in FIG. 5.
한계직각프리즘 산출단계(S20)는 산출하고자 하는 직각프리즘에 대한 계산 한계를 정의하는 단계이다.The marginal right angle prism calculation step (S20) is a step of defining a calculation limit for the right angle prism to be calculated.
한계직각프리즘은 말단장치 도달가능위치의 x축방향의 최대치와 최소치, y 축방향의 최대치와 최소치, z 축방향의 최대치와 최소치에 의해 정의된다.The limiting right angle prism is defined by the maximum and minimum values in the x-axis direction of the end device reachable position, the maximum and minimum values in the y-axis direction, and the maximum and minimum values in the z-axis direction.
이러한 한계직각프리즘에는 다축기계의 말단장치가 도달불가능한 영역도 포함되어 있다. 따라서 최대직각프리즘 작업공간을 산출함에 있어서 한계직각프리즘 이상의 공간에 대해서는 검토할 필요가 없다.The marginal right angle prism also includes a region where the end device of a multi-axis machine is unreachable. Therefore, it is not necessary to examine the space above the limiting right-angle prism in calculating the maximum right-angle prism working space.
한계직각프리즘은 아래와 같은 식으로 표현할 수 있다.The marginal right angle prism can be expressed by the following equation.
Figure PCTKR2019002551-appb-I000001
Figure PCTKR2019002551-appb-I000001
여기서 VTEMP 는 한계직각프리즘 영역이고, xmax 은 말단장치 도달가능위치의 x축방향의 최대치이고, xmin 은 말단장치 도달가능위치의 x축방향의 최소치이고, ymax 은 말단장치 도달가능위치의 y축방향의 최대치이고, ymin 은 말단장치 도달가능위치의 y축방향의 최소치이고, zmax 은 말단장치 도달가능위치의 z축방향의 최대치이고, zmin 은 말단장치 도달가능위치의 z축방향의 최소치이다.Where V TEMP Is the marginal right-angle prism area, x max Is the maximum value in the x-axis direction of the end device reachable position, x min Is the minimum value in the x-axis direction of the end device reachable position, y max Is the maximum value in the y-axis direction of the end device reachable position, y min Is the minimum value in the y-axis direction of the reachable end device, z max Is the maximum value in the z-axis direction of the end device reachable position, and z min is the minimum value in the z-axis direction of the end device reachable position.
만약 워크테이블의 위치가 결정되어 있다면 Zmin 값 대신 ZWorktable로 다음과 같이 정의될 수 있을 것이다.If the location of the worktable is determined, it can be defined as ZWorktable instead of Zmin value.
Figure PCTKR2019002551-appb-I000002
Figure PCTKR2019002551-appb-I000002
공간분할단계(S30)는 한계직각프리즘을 복수의 분할체적으로 분할하는 단계이다.The space division step (S30) is a step of dividing the marginal right angle prism into a plurality of divided volumes.
공간분할단계(S30)의 분할체적으로는 직육면체 형상을 채택하는 것이 바람직하다.It is preferable to adopt a rectangular parallelepiped shape as the divided volume of the space division step (S30).
분할체적의 크기는 컴퓨터의 계산능력을 고려하여 적절히 선정할 수 있다.The size of the divided volume can be appropriately selected in consideration of the computing power of the computer.
도달가능여부 판단단계(S40)는 상기 공간분할단계(S30)에서 분할된 분할체적의 각 꼭지점이 상기 말단장치에 의해 도달가능한지 여부를 판단하는 단계이다.The reachability determining step S40 is a step of determining whether each vertex of the divided volume divided in the space dividing step S30 is reachable by the end device.
도달가능여부 판단단계(S40)에서는 분할체적의 각 꼭지점에 위치하기 위한 각 구동축의 이송거리와 회전각도가 구동축이 구현가능한 영역에 포함되는지 여부에 따라 결정된다.In the reachability determination step (S40), the transport distance and rotation angle of each drive shaft to be located at each vertex of the divided volume are determined according to whether the drive shaft is included in the implementable region.
분할체적의 각 꼭지점에 위치하기 위한 각 구동축의 이송거리와 회전각도는 다축기계에 대한 역기구학 계산에 의해 얻어진다.The feed distance and rotation angle of each drive shaft to be located at each vertex of the divided volume are obtained by inverse kinematic calculations for a multi-axis machine.
여기서 역기구학 계산이란 다축기계 말단장치의 주어진 위치를 구현하기 위해 각 구동축의 이동거리와 회전각도를 산출하는 것을 말한다.Here, the inverse kinematic calculation refers to calculating the moving distance and rotation angle of each drive shaft to realize a given position of the multi-axis machine end device.
결과적으로 분할체적의 각 꼭지점은 다축기계의 말단장치가 도달가능한 점인지 도달불가능한 점인지 판단된다.As a result, each vertex of the divided volume is determined whether the end device of the multi-axis machine is reachable or unreachable.
마지막으로 최대직각프리즘 산출단계(S50)가 수행된다.Finally, the step of calculating the maximum right-angle prism (S50) is performed.
최대직각프리즘 산출단계(S50)는 한계직각프리즘에 포함되는 직각프리즘으로서, 상기 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출하는 단계이다.The maximum right-angle prism calculating step S50 is a right-angle prism included in the limit right-angle prism, and is a step of calculating a right-angle prism having a maximum size reachable by the terminal device.
최대직각프리즘 산출단계(S50)에서는 우선 분할체적을 직육면체 형상으로 조합한 중간단계의 직각프리즘을 형성한다.In the step of calculating the maximum right-angle prism (S50), first, a right-angle prism in an intermediate step in which the divided volume is combined into a rectangular parallelepiped shape is formed.
상기 중간단계 직각프리즘을 구성하는 꼭지점 중에 상기 도달가능여부 판단단계(S40)에서 말단장치가 도달불가능한 것으로 판단된 꼭지점이 포함되지 않도록 중간단계 직각프리즘을 점진적으로 확장시켜 나간다.Among the vertices constituting the intermediate step right angle prism, the intermediate step right angle prism is gradually expanded so that the vertex determined by the end device to be unreachable is not included in the step S40 of determining whether it is reachable.
이 때 최대직각프리즘 산출단계(S50)는 중간단계 직각프리즘을 한계직각프리즘까지 확장시키면서 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출한다.At this time, in the step of calculating the maximum right angle prism (S50), the right angle prism of the maximum size reachable by the end device is calculated while the intermediate right angle prism is extended to the limit right angle prism.
최대직각프리즘 산출단계(S50)에서는 다축기계 구동축의 대칭조건을 반영하여 중간단계 직각프리즘을 형성함으로써 계산시간을 줄일 수 있다.In the step of calculating the maximum right-angle prism (S50), the calculation time can be reduced by forming the intermediate-level right-angle prism by reflecting the symmetry condition of the multi-axis machine drive shaft.
또한 최대직각프리즘 산출단계(S50)에서는 다축기계의 공작물 테이블 위치를 반영하여 중간단계 직각프리즘을 형성함으로써 계산시간을 줄일 수 있다.In addition, in the step of calculating the maximum right-angle prism (S50), the calculation time can be reduced by forming the intermediate-level right-angle prism by reflecting the position of the workpiece table of the multi-axis machine.
즉, 공작물 테이블 보다 낮은 높이로는 작업이 이뤄질 수 없으므로, 공작물 테이블 위치보다 낮은 영역은 계산에서 배제함으로써 계산시간을 줄일 수 있다.That is, since the work cannot be performed at a height lower than the work table, the calculation time can be reduced by excluding an area lower than the work table position from the calculation.
본 발명에 따른 다축기계의 최대직각프리즘 작업공간 산출방법은 다축기계의 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출함으로써, 가공품의 설계단계 및 공정준비단계에서 작업 공간 제약으로 인한 공정가능여부를 쉽게 확인할 수 있는 동시에, 다축기계 설계 시에 최대한의 작업공간을 확보할 수 있도록 테이블 및 구조물의 배치를 결정하는 정량적 기준을 제공하는 효과가 있다.The method for calculating the maximum right-angle prism working space of a multi-axis machine according to the present invention calculates the right-angle prism of the largest size reachable by the end device of the multi-axis machine, thereby enabling processability due to work space limitations in the design stage and process preparation stage of the workpiece. At the same time, it has the effect of providing a quantitative criterion for determining the arrangement of tables and structures so as to ensure the maximum working space when designing a multi-axis machine.
이상에서는 본 발명의 바람직한 실시예에 대하여 도시하고 설명하였지만, 본 발명은 상술한 특정의 실시예에 한정되지 아니하며, 청구범위에서 청구하는 본 발명의 요지를 벗어남이 없이 당해 발명이 속하는 기술분야에서 통상의 지식을 가진 자에 의해 다양한 변형실시가 가능한 것은 물론이고, 이러한 변형 실시예들은 본 발명의 기술적 사상이나 전망으로부터 개별적으로 이해되어서는 안 될 것이다.In the above, preferred embodiments of the present invention have been illustrated and described, but the present invention is not limited to the specific embodiments described above, and it is usually in the technical field to which the present invention belongs without departing from the gist of the present invention claimed in the claims. It is of course possible to perform various modifications by a person having knowledge of, and these modified embodiments should not be individually understood from the technical idea or prospect of the present invention.

Claims (8)

  1. 다축기계에서 작업가능한 직육면체 형상의 최대작업공간을 산출하는 방법에 있어서,In the method for calculating the maximum working space of a rectangular parallelepiped shape that can work in a multi-axis machine,
    다축기계의 말단장치가 도달가능한 위치좌표를 산출하는 말단장치 도달가능위치 산출단계(S10);An end device reachable position calculating step (S10) of calculating a position coordinate reachable by the end device of the multi-axis machine;
    상기 말단장치 도달가능위치의 x축방향의 최대치와 최소치, y 축방향의 최대치와 최소치, z 축방향의 최대치와 최소치에 의해 정의되는 한계직각프리즘을 산출하는 한계직각프리즘 산출단계(S20);A limiting right angle prism calculating step (S20) for calculating a limiting right angle prism defined by a maximum value and a minimum value in the x-axis direction, a maximum value and a minimum value in the y-axis direction, and a maximum value and a minimum value in the z-axis direction of the reachable position of the end device;
    상기 한계직각프리즘을 복수의 분할체적으로 분할하는 공간분할단계(S30);A space division step (S30) of dividing the marginal right angle prism into a plurality of divided volumes;
    상기 분할체적의 각 꼭지점이 상기 말단장치에 의해 도달가능한지 여부를 판단하는 도달가능여부 판단단계(S40);A reachability determining step (S40) for determining whether each vertex of the divided volume is reachable by the end device;
    상기 한계직각프리즘에 포함되는 직각프리즘으로서, 상기 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출하는 최대직각프리즘 산출단계(S50);를 포함하는, 다축기계의 최대직각프리즘 작업공간 산출방법Comprising a maximum right angle prism included in the limiting right angle prism, a maximum right angle prism calculating step (S50) of calculating a right angle prism of the maximum size reachable by the end device;
  2. 제1항에 있어서,According to claim 1,
    상기 말단장치 도달가능위치 산출단계(S10)는 다축기계 각 구동축의 가능한 이송거리와 회전각도를 조합하여 상기 다축기계에 대한 정기구학 계산에 의해 말단장치의 도달가능위치를 산출하는 것을 특징으로 하는, 다축기계의 최대직각프리즘 작업공간 산출방법The end device reachable position calculation step (S10) is characterized in that the reachable position of the end device is calculated by a static kinematic calculation of the multi-axis machine by combining the possible feed distance and rotation angle of each drive shaft of the multi-axis machine, How to calculate the maximum right angle prism working space of a multi-axis machine
  3. 제1항에 있어서,According to claim 1,
    상기 공간분할단계(S30)의 분할체적은 직육면체 형상인 것을 특징으로 하는, 다축기계의 최대직각프리즘 작업공간 산출방법A method of calculating the maximum right-angle prism working space of a multi-axis machine, characterized in that the divided volume of the space dividing step (S30) is a rectangular parallelepiped shape.
  4. 제1항에 있어서,According to claim 1,
    상기 도달가능여부 판단단계(S40)는 상기 다축기계에 대한 역기구학 계산에 의해 계산된 말단장치가 상기 분할체적의 각 꼭지점에 위치하기 위한 각 구동축의 이송거리와 회전각도가 구현가능한 영역에 포함되는지 여부에 따라 결정되는 것을 특징으로 하는, 다축기계의 최대직각프리즘 작업공간 산출방법The reachability determining step (S40) is whether the end device calculated by the inverse kinematics calculation for the multi-axis machine is included in a region where the transport distance and rotation angle of each drive shaft to be located at each vertex of the divided volume are implemented. Method of calculating the maximum right angle prism working space of a multi-axis machine, characterized in that it is determined according to whether or not
  5. 제1항에 있어서,According to claim 1,
    상기 최대직각프리즘 산출단계(S50)는 상기 분할체적을 직육면체 형상으로 조합한 중간단계의 직각프리즘을 형성하고, 상기 중간단계 직각프리즘을 구성하는 꼭지점 중에 상기 도달가능여부 판단단계(S40)에서 말단장치가 도달불가능한 것으로 판단된 꼭지점이 포함되지 않도록 중간단계 직각프리즘을 확장시키는 것을 특징으로 하는, 다축기계의 최대직각프리즘 작업공간 산출방법The maximum right-angle prism calculation step (S50) forms an intermediate-level right-angle prism by combining the divided volumes into a rectangular parallelepiped shape, and an end device in the reachability determination step (S40) among vertices constituting the intermediate-level right-angle prism. A method for calculating the maximum right-angle prism working space of a multi-axis machine, characterized in that the intermediate-level right-angle prism is extended so that the vertex determined to be unreachable is not included.
  6. 제5항에 있어서,The method of claim 5,
    상기 최대직각프리즘 산출단계(S50)는 상기 중간단계 직각프리즘을 한계직각프리즘까지 확장시키면서 상기 말단장치에 의해 도달가능한 최대 크기의 직각프리즘을 산출하는 것을 특징으로 하는, 다축기계의 최대직각프리즘 작업공간 산출방법The maximum right-angle prism calculation step (S50) is characterized in that the right-angle prism having a maximum size reachable by the end device is expanded while extending the intermediate-stage right-angle prism to the limit right-angle prism. Calculation method
  7. 제5항에 있어서,The method of claim 5,
    상기 최대직각프리즘 산출단계(S50)는 상기 다축기계 구동축의 대칭조건을 반영하여 상기 중간단계 직각프리즘을 형성함으로써 계산시간을 줄이는 것을 특징으로 하는, 다축기계의 최대직각프리즘 작업공간 산출방법The maximum right-angle prism calculation step (S50) is characterized by reducing the calculation time by forming the intermediate-stage right-angle prism by reflecting the symmetry condition of the multi-axis machine driving shaft, and calculating the maximum right-angle prism working space of the multi-axis machine
  8. 제5항에 있어서,The method of claim 5,
    상기 최대직각프리즘 산출단계(S50)는 상기 다축기계의 공작물 테이블 위치를 반영하여 상기 중간단계 직각프리즘을 형성함으로써 계산시간을 줄이는 것을 특징으로 하는, 다축기계의 최대직각프리즘 작업공간 산출방법The maximum right-angle prism calculation step (S50) is characterized by reducing the calculation time by forming the intermediate-stage right-angle prism by reflecting the position of the workpiece table of the multi-axis machine, calculating the maximum right-angle prism working space of the multi-axis machine
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