Mechanical Design Handbook

In post [ Timing Diagram (Part 1 - No Overlap Movement) ], we established the design requirement: The die must work synchronously with the indexing mill. The Problem: Rigid Sequencing Without detailed calculation, inexperienced designers often end up with a rigid timing diagram. The die waits for the indexing to completely finish before moving. This compressed movement window results in extremely high acceleration (4.15 m/s 2 ), leading to high inertial forces and premature equipment failure . The Solution: Optimized Overlap In post [ Part 3 - Cycloid Cam Profile Analysis ], we analyzed the "Soft Start" properties of the Cycloid profile. By allowing the motions to overlap safely, we extended the indexing angle significantly. The Engineering Impact: We calculated that the maximum acceleration for this new timing diagram is 5 times lower than the original. This is the power of Motion Simulation . Visu...

In the previous post [ Timing Diagram (Part 2 - Maximum acceleration calculation) ], we calculated the maximum acceleration of the die using a cycloid cam profile. We discovered that the inertial forces are inversely proportional to the square of the indexing time. This means if we can extend the indexing angle (B m ) through overlap motion , we can drastically reduce wear. This is a key strategy in Predictive Maintenance —designing machines that inherently last longer. Cycloid Cam Profile Analysis The Cycloidal motion cam profile has the following movement equation: h = h m × [ t/t m - 1/(2π) × sin(2π × t/t m ) ] Rearranging the equation to solve for the displacement ratio: h / h m = t/t m - 1/(2π) × sin(2π × t/t m ) The "Soft" Start and Stop: Looking at the graph above, notice that at the first 10% of the time, the movement is only 0.65% of the total stroke. Similarly, in the final ...

In the previous post [ Timing Diagram (Part 1 - No Overlap Movement) ], we determined that without overlap, our die must travel 50mm within a tight cam angle of just 55 degrees. Now, we must ask: What is the physical cost of this rapid movement? To answer this, we calculate the Maximum Acceleration . In Machine Dynamics , acceleration is directly proportional to Force (F = m × a). High acceleration means high inertial forces, which lead to severe wear, vibration, and the need for expensive oversized servo motors . Step 1: The Time Calculation First, we need to convert our "Cam Angle" into actual "Time" in seconds. Let: N = Machine Speed (pieces per hour) B m = Indexing Angle (degrees) Cycle time (sec) = 3600 / N Indexing time t m = (B m / 360) × Cycle time Indexing time t m = (B m / 360) × (3600 / N) t m (sec) = (10 × B m ) / N Step 2: Cycloid Cam Profile Equations The die moves using a Cycloid Cam Prof...

When you search Google for " timing diagram ", you typically find results about electrical timing diagram software for digital logic or PLC programming. However, in the context of Mechanical Machine Design , a Timing Diagram is a critical tool that represents the sequential movement of mechanisms. It is an essential visualization for engineers to understand how each part of an industrial automation system works in synchronization. By properly designing the timing diagram, we can make machine moves smoother even at higher speeds, significantly reducing operational costs. We typically draw the timing diagram using the Cam Angle (degrees) on the horizontal axis and the Mechanism Movement (mm) on the vertical axis. The Goal: Reducing Wear and Maintenance Costs From the timing diagram, we can identify opportunities to reduce the acceleration (and thus the inertial force) of moving parts. Experience shows that many mechanisms are designed wi...

In the previous post ( Standards of limits and fits for mating parts ), we defined the core terms of the ISO 286 standard . Now, we translate that theory into real-world Precision Metrology calculations. While manual math is good for understanding the "why," modern manufacturing relies on Tolerance Analysis Software to prevent costly scrap in CNC Machining . Automated Calculation Logic Below is an example of how logic is structured in engineering spreadsheets or professional Quality Control (QC) software to determine upper and lower deviations. Step-by-Step Manual Calculation Let's verify the software's logic by calculating the deviations manually. Example: Calculate the deviations for a shaft with a diameter of 40 mm and a tolerance class of g6 (40g6). Step 1: Determine the Geometric Mean (D) First, we find the basic size range. For a 40 mm shaft, the range is "Over 30 up to 50 mm" (D_min = 30, D_max = 50)....