## 5 Method for Designing Manipulators for Man-Portable UGVs
### Load Cases Definition  
In the next stage of the procedure, the manipulator selected from the Pareto front is analyzed to identify the maximum loads that may occur in its structure. These loads can be grouped into two categories: those that remain constant regardless of the manipulator's configuration, and those that vary according to configuration. For joint bodies, the loads stemming from the worm gear drive are transmitted via the contact surfaces of the worm and worm wheel bearings. When the gearbox operates at maximum torque, the magnitudes and directions of these loads depend solely on the drive's direction of operation (two possible orientations). Additional loads--such as the forces and moments acting on the joint bearings that also support the worm gear wheel--fluctuate based on the manipulator's configuration. To determine their maximum values, one must consider scenarios in which the movement of the manipulator tip is obstructed (e.g., by an obstacle). Under these conditions, with the manipulator drives at maximum torque, the joint loads will depend strongly on the manipulator's specific configuration. Identifying these peak loads for various orientations is essential for the subsequent component optimization stage. As an example, the maximum joint loads can be tested on a typical five-degree-of-freedom (5R) manipulator structure designed for EOD robots where all joints are rotary. The structure of the manipulator is shown in Figure 2. It consists of the following elements: element 1, the drive moving the manipulator in vertical axis 1; element 2 driven by a joint with axis 2 perpendicular to the axis of element 1; elements 3 and 4 with drives on axes parallel to axis 2; and element 5, a gripper that can rotate around its longitudinal axis, perpendicular to drive axis 4. During the analysis, the structure of the manipulator is simplified by locking the rotation in axis 1 so all the elements move in a common plane. The structure will be considered as a flat mechanism, which is sufficient for performing load analysis. The maximum loads in the event of a collision of the manipulator gripper with an obstacle can be determined by searching for a manipulator configuration that will cause maximum loads when trying to move the joints with the maximum torque while the movement of the tip of the gripper is blocked. It can be noticed that, after blocking  
Figure 2: Simplified model of 5-DOF manipulator. the gripper's movement, the moments generated in axes 2, 3, and 4 do not have radial components in these axes and the axial components cannot be greater than the maximum torque transferred by the overload clutches of these joints. The situation is different in the case of the driving torque in axis 1. When the gripper is blocked, radial moment loads are generated in joints 2, 3, and 4, the value of which depends only on the manipulator configuration. These load components of joints 2, 3, and 4 are not limited by overload clutches, but when the load limit is exceeded, the robot will fall over, which will prevent further load increase. The example of manipulator joint 3 will show how to calculate the load in the direction we are interested in. Let us assume that drive 1 of the manipulator operates with the torque \(M_{1}\) and the gripper rests against an obstacle so the movement is blocked. The value of the force \(F\) that is exerted on the obstacle is as follows:  
\[F=\frac{M_{1}}{L_{2}\cdot s_{2}+L_{3}\cdot s_{23}+L_{4}\cdot s_{234}} \tag{1}\]  
where \(L_{2},L_{3},L_{4}\) are the distances between joints 2 and 3, 3 and 4, and 4 and the end of the gripper (Figure 2); \(s_{2},s_{23},s_{234}\) are simplified notifications of \(sin(q1),sin(q1+q2),sin(q1+q2+q3)\); and \(q2,q3,q4\) are the internal coordinates of the manipulator's joints. In joint 3, the torque resulting from the force F acting on the arm equal to the distance of joint 3 from the end of the gripper (Figure 2), marked as \(M_{F}3\), is  
\[M_{F3}=