Mechanical Design Handbook

This is the moment of truth. In the previous posts, we moved from abstract mathematical derivations in Excel to the concrete setup of a 3D Digital Twin . The result of our timing diagram design—utilizing overlapping motion with Fifth-Degree (3-4-5) Polynomial and Linear cam functions—is now fully integrated into the 3D model. The Power of "Spreadsheet Run" The simulation below was executed using the Kinematics environment in the Unigraphics (UG) NX4 Motion Simulation Module . By utilizing the "Spreadsheet Run" command, we are not just animating the assembly; we are driving the geometry with pure data. Every frame of movement corresponds to a specific calculation row in our Excel sheet. This confirms that the complex polynomial curves we designed will physically clear the tooling without collision. Video Analysis: Virtual Commissioning Watch the simulation below closely. Unlike the "Constant Velocity" test in Part 3 (which r...

In [ Part 3 of this series ], we set up the kinematic joints for our machine. However, the drivers are currently set to "Constant Velocity," which does not reflect reality. Now, we execute the most powerful part of the Digital Twin workflow: injecting our precise timing diagram data from Excel directly into the 3D simulation. Step 1: Exporting Joint Data to Excel 1. Select the "Graphing" command. This tool is typically used to view results, but we will use it to open the data channel. 2. Select "Spreadsheet" . This tells NX to bridge the data into Microsoft Excel. 3. Click OK. NX will automatically launch Excel. You will see columns for "drv J_Mill" and "drv J_Die" with linear values. These are the default placeholders we created earlier. We must replace these with our optimized curves. Step 2: Preparing the Data Pro Tip: Do ...

In [ Part 2 of this series ], we finished setting the driver for the revolute joint of the indexing mill. Now, we will set up the Punch Die . Step 1: Setting up the Slider Joint The movement of the punch die is different from the indexing mill. It moves only in linear motion along the Z-axis. The joint for this kind of movement is called a "Slider" joint. Procedure: 1. Select Joint command. 2. Select "Slider" joint icon. 3. Select the "Die" link we created earlier. 4. Click "Orientation on the first link" → Select "Point". 5. Select the center point of the cylinder to define the joint origin. 6. Select "Vector" → Click the bottom face of the cylinder (defines the downward Z-axis). 7. Rename to "J_Die". 8. Click Ok. Step 2: Defining the Linear Driver 1. Right-click joint "J_Die" → Edit. ...

Let's continue from the previous post . Now it's time to visualize our previous calculation for the timing diagram of the indexing mill and punch die using 3D Motion Simulation in Unigraphics (UG) NX4 . While we successfully created a 2D motion simulation in Excel , modern engineering demands a full Digital Twin . The UG NX4 Assembly model is prepared as shown below. The mating conditions of the assembly model follow the sketch shown in [ Timing Diagram (Part 1 - No Overlap Movement) ]. Step 1: Entering the Simulation Environment New to UG NX4 Motion Simulation ? No problem. Follow this step-by-step guideline. In the motion simulation environment , all commands are initially disabled. You must right-click on the assembly file and select New Simulation . This command creates the necessary files and organizes them automatically. Step 2: Defining the Kinematic Environment ...

During the process of timing diagram design , I normally start with detailed calculations in an Excel spreadsheet to minimize acceleration while satisfying the required process cycle time. Once I can visualize the preferred displacement, velocity, and acceleration profiles of the mechanisms in Excel, the question becomes: What's next? Shall I start manufacturing immediately? The answer is NO. In modern engineering, we use Digital Twin Technology to verify the design first. From Excel to 3D Simulation Currently, I use Unigraphics (UG) NX4 (now Siemens NX) to design the mechanical parts. When the assembly modeling is done, I use the assembly model to simulate the movement of mechanisms with the Motion Simulation Module . This step is critical for Virtual Commissioning . It helps confirm the timing diagram before releasing the design for manufacturing. It is especially useful when movements are combined in 3D space, allowing me to detect ...

In the post [ Polynomial Cam Function (Part 3) ], we explored the characteristics of the 5th-degree profile. Now, we put it to work. We will revisit the same die-press example from [ Timing Diagram (Part 4) ]. Originally, without overlap, the acceleration was a massive 4.154 m/s 2 . Using a Cycloid profile with overlap, we reduced it to 0.804 m/s 2 . This time, we will use a Fifth-Degree (3-4-5) Polynomial combined with a Linear Cam Function . While the peak acceleration reduction might be similar to the Cycloid, the real advantage here is control —specifically, the ability to blend different motion segments seamlessly without stopping. The Motion Strategy Our constraints remain the same: Total displacement is 50 mm, and the die must dwell inside the hole for 30 mm. Unit Conversion Note: The equations we derived calculate velocity in mm/rad . To convert to real-world time domain: • Velocity (mm/s) = Velocity (mm/rad) × ω (rad/s) • Acceleration (mm/s 2 ...

In [ Polynomial Cam Function (Derivation of Fifth-degree function) - Part 2 ], we derived the equations for the Fifth-Degree (3-4-5) Polynomial . Now, we apply this math to the real world of Mechanical Cam Design . The shape of the physical cam is determined by plotting these functions. Unlike a standard Cycloid curve, the polynomial allows us to manipulate the Start Velocity (v 0 ) and End Velocity (v 1 ) of the follower. However, this flexibility requires careful design. If the coefficients are not balanced, the physical cam profile can develop "dips" or negative slopes, causing the mechanical linkage to behave unpredictably. Case 1: Standard Dwell-to-Dwell (Zero Velocity) Here, we set v 0 = 0 and v 1 = 0 . Visually, this looks identical to a Cycloid curve. It is the safest profile for standard cam applications where the follower starts from a dwell (rest) and ends at a dwell. Case 2: The "Dip" Danger (Negative Displa...

In [ Polynomial Cam Function (Introduction) - Part 1 ], we discussed the fundamental law of cam design: continuity of acceleration. In this post, we are going to derive the exact equations for the Fifth-Degree Polynomial Cam Function . This is the "secret sauce" used in Motion Control Algorithms for high-end servo drives to ensure smooth, jerk-free movement. The General Equations We start with the general polynomial equation. To make the math handleable, we normalize the input angle as a ratio (b / b m ) . s = C 0 + C 1 (x) + C 2 (x) 2 + C 3 (x) 3 + C 4 (x) 4 + C 5 (x) 5 Where: s = Displacement (mm) x = Ratio of cam angle (b / b m ) b = Current cam angle (rad) b m = Total angle in sector (rad) To find Velocity (v) and Acceleration (a) , we differentiate with respect to the angle. (Note: v is in mm/rad. To convert to mm/s, multiply by angular velocity ω) Velocity Equation (v = ds/db): v = (1/b m ) × [ C 1 + 2C 2 (x) + ...