关于机械手的中英文翻译

separation between the two parts. R1?R2??0,0，0,0,0,1?, and so, the degree of freedom around the z axis will be ignored in the following steps.

In the case that there is a loop in the relation graph, such as parts Part 5, Part 6, and Part 7 in Fig. 2, the loop has to be broken before the mating direction is calculated. Under the assumption that all parts in the CAD model are fully constrained and not over-constrained, the following simple approach is adopted. For the part t in the loop, calculate the number of 1s in

Nti?Ri1?Ri2?...?Rin; where Rik is the remaining degrees of freedom of constraint k by part i. For example, in Fig. 2, given that the number of 1s inUpart5,part7 and Upart6,part7 is larger than

Upart5,part6 and Upart6,part5, respectively, then it can be regarded that the position of Part 7 is determined by constraints with both Part 5 and Part 6, while Part 5 and Part 6 can be fully constrained by constraints between Part 5 and Part 6.We can unite Part 5 and Part 6 as one node in the relation graph, also called a composite node, as shown in Fig. 2b. The composite node will be regarded as a single part, but it is obvious that the composite node implies an assembly sequence.

2. Calculate mating directions for all nodes in the relation graph. Again, beginning at the state that the shaft and the hole are assembled, separate the part in one degree of separation by a certain distance (larger than the maximum tolerance), and then check if interference occurs. Separation in both ±x axis and ±y axis of R1 causes the interference between the shaft and the hole. Separation in the +z direction raises no interference. Then, select the +z direction as the mating direction, which is represented as a vector M measured in the coordinate system of the assembly. It should be noted that, in some cases, there may be several possible mating directions for a part. The condition for assembly operation in the mating direction to be ended should be given. When contact occurs between parts in the mating direction at the assembled state, which can be checked simply with geometric constraints, the end condition is measured by force sensory information, whereas position information is used as an end condition.

3. Calculate the grasping position. In this paper, parts are handled and manipulated with two separate probes, which will be discussed in the Sect. 4, and planes or edges are considered for grasping. In the case that there are several mating directions, the grasping planes are selected as G1∩G2∩...∩Gi, where Gi is possible grasping plane/edge set for the ith mating direction when the part is at its free state. For example, in Fig. 4, the pair planes P1/P1′, P2/P2′, and P3/P3′ can serve as possible grasping planes, and then the grasping planes are

Gmating_dir1?Gmating_dir2?Gmating_dir3??P1/P1?,P2/P2?,P3/P3????P1/P1?,P3/P3????P1/P1?,P2/P2????P1/P1??

The approaching direction of the end-effector is selected as the normal vector of the

grasping planes. It is obvious that not all points on the grasping plane can be grasped. The following method is used to determine the grasping area. The end-effector, which is modeled as a cuboid, is first added in the CAD model, with the constraint of coplanar or tangential with the grasping plane. Beginning at the edge that is far away from the Base_Part in the mating direction, move the end-effector in the mating direction along the grasping plane until the end-effector is fully in contact with the part, the grasping plane is fully in contact with the end-effector, or a collision occurs. Record the edge and the distance, both of which are measured in the part’s coordinate system.

4. Separate gradually the two parts along the mating direction, while checking interference in the other degrees of separation, until no interference occurs in all of the other degrees of separation. There is obviously a separation distance that assures interference not to occur in every degree of separation. It is called the safe length in that direction. This length is used for the collision-free path calculation, which will be discussed in the following section. 2.2 Assembly sequence

Some criteria can be used to search the optimal assembly sequence, such as the mechanical stability of subassemblies, the degree of parallel execution, types of fixtures, etc. But for microassembly, we should pay more attention to one of its most important features, the limited workspace, when selecting the assembly sequence. Microassembly operations are usually conducted and monitored under microscopy, and the workspace for microassembly is very small. The assembly sequence brings much influence on the assembly efficiency. For example, a simple assembly with three parts. In sequence a, part A is first fixed onto part B. In the case that part C cannot be mounted in the workspace at the same time with component AB because of the small workspace, in order to assemble part C with AB, component AB has to be unmounted from the workspace. Then, component C is transported and fixed into the workspace. After that, component AB is transported back into the workspace again. In sequence b, there is no need to unmount any part. Sequence a is obviously inefficient and may cause much uncertainty. In other words, the greater the number of times of unmounting components required by an assembly sequence, the more inefficient the assembly sequence. In this paper, due to the small -workspace feature of microassembly, the number of times necessary for the mounting of parts is selected as the search criteria to find the assembly sequence that has a few a number of times for the mounting of parts as possible.

This paper proposes the following approach to search the assembly sequence. The relation graph of the assembly is used to search the optimal assembly sequence. Heuristic approaches are adopted in order to reduce the search times:

1. Check nodes connected with more than two nodes. If the mating directions of its connected nodes are different, mark them as inactive nodes, whereas mark the same mating directions as active mating direction.

2. Select a node that is not an inactive node. Mark the current node as the base node (part). The first base part is fixed on the workspace with the mating direction upside (this is done in the CAD model). Compare the size (e.g., weight or volume) of the base part with its connected parts, which can be done easily by reading the bill of materials (BOM) of the assembly. If the base part is much smaller, then mark it as an inactive node.

3. Select a node connected with the base node as an assembly node (part). Check the mating direction if the base node needs to be unmounted from the workspace. If needed, update a variable, say mount++. Reposition the component (note that there may be not only the base part in the workspace; some other parts may have been assembled with the base part) in the workspace so that the mating direction is kept upside.

4. In the CAD model, move the assembly part to the base part in the possible mating direction, while checking if interference (collision) occurs. If interference occurs, mark the base node as an inactive node and go to step 2, whereas select the Operation type according to parts’ geometric features. In this step, an Obstacle Box is also computed. The box, which is modeled as a cuboid, includes all parts in the workspace. It is used to calculate the collision-free path to move the assembly part, which will be introduced in the following section. The Obstacle Box is described by a position vector and its width, height, and length.

5. Record the assembly sequence with the Operation type, the mating direction, and the grasping position.

6. If all nodes have been searched, then mark the first base node as an inactive node and go to step 2. If not, select a node connected with the assembly node. Mark it as an assembly node, and the assembly node is updated as a base node. Check if there is one of the mating directions of the assembly node that is same as the mating direction of the former assembly node. If there is, use the former mating direction in the following steps. Go to step 3.

After searching the entire graph, we may have several assembly sequences. Comparing the values of mount, the more efficient one can be selected. If not even one sequence is returned, then users may have to select one manually. If there are N nodes in the relation graph of Fig. 2b, all of which are not classed as inactive node, and each node may have M mating directions, then it needs MN computations to find all assembly sequences. But because, usually, one part only has one mating direction, and there are some inactive nodes, the computation should be less than MN.

It should be noted that, in the above computation, several coordinate systems are involved, such as the coordinates of the assembly sequence, the coordinates of the base part, and the

coordinates of the assembly. The relations among the coordinates are represented by a 4×4 transformation matrix, which is calculated based on the assembly CAD model when creating the relations graph. These matrixes are stored with all of the related parts in the database. They are also used in skill decomposition.

3 Skill decomposition and execution

3.1 Definition of skill primitive

Skill primitives are the interface between the assembly planning and robot control. There have been some definitions on skill primitives. The basic difference among these definitions is the skill’s complexity and functions that one skill can fulfill. From the point of view of assembly planning, it is obviously better that one skill can fulfill more functions. However, the control of a skill with many functions may become complicated. In the paper, two separate probes, rather than a single probe or parallel jaw gripper, are used to manipulate the part. Even for the grasp operation, the control process is not easy. In addition, for example, moving a part may involve not only the manipulator but also the worktable. Therefore, to simplify the control process, skills defined in the paper do not include many functions.

More importantly, the skills should be easily applied to various assembly tasks, that is, the set of skills should have generality to express specific tasks. There should not be overlap among skills. In the paper, a skill primitive for robot control is defined as:

Attribute_i,Action_i?Attribute_i?,Si?Start_i?Attribute_i?,End_i?Attribute_i?,

Condition_i?Attribute_i?Attributes_i Information necessary for Si to be executed. They can be classified as required attributes and option attributes, or sensory attributes and CAD-model-driven attributes. The attributes are represented by global variables used in different layers.

Action_i Robots’ actions, which is the basic sensormotion. Many actions are defined in the system, such as Move_Worktable, Move_Probes, Rotation_Worktable, Rotation_Probes, Touch, Insert, Screw, Grasp, etc. For one skill, there is only one Action. Due to the limited space, the details of actions will not be discussed in this paper.

Start_i The start state of Action_i, which is measured by sensor values. End_i The end state of Action_i, which is measured by sensor values. Condition_i The condition under which Action_i is executed.

From the above definitions, we may find that skill primitives in the paper are robot motions with start state and end state, and that they are executed under specific conditions. Assembly