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Showing posts with the label cam design

Excel VBA Kinematic Simulation: Overlapping Motion in High-Speed Machines

The Engineering Challenge: In 2005, I was tasked with upgrading a mechanical transfer turret used to handle highly fragile glass tubes between a conveyor and another process. Production demanded a 25% throughput increase—jumping from 1,200 UPH (Units Per Hour) to 1,500 UPH. Simply speeding up the main drive motor was impossible; the resulting inertial forces and acceleration spikes would have violently shattered the glass tubes before they ever reached the sealing station. The Solution: When you need to increase machine throughput without increasing acceleration forces, the answer is almost always overlapping motion . However, overlapping mechanisms in tight spaces introduces a severe risk of catastrophic mechanical collisions. To validate this 25% speed increase safely, I didn't use expensive 3D motion analysis software. Instead, I used Microsoft Excel and VBA to build a custom 2D kinematic simulator. Here is how that mathematical model was built, and how that exact m...

Polynomial Cam Design: Die-Press Simulation (Part 4)

In the post [ Polynomial Cam Function (Part 3) ], we explored the characteristics of the 5th-degree profile. Now, we put it to work. Advertisement 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)...

Polynomial Cams: Analysis & Design Pitfalls (Part 3)

Figure 1: Mathematical coefficients determine the physical shape. Poor math leads to physical defects like the "dip" shown on the right. In [ Polynomial Cam Function (Derivation of Fifth-degree function) - Part 2 ], we derived the equations for the Fifth-Degree (3-4-5) Polynomial . Advertisement 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) Figure 2: The standard profile (v 0 =0, v 1 =0). Safe, smooth, and ide...

5th-Degree Polynomial Cam Curve Derivation (Part 2)

Figure 1: Deriving the "secret sauce" of smooth motion control requires calculus. In [ Polynomial Cam Function (Introduction) - Part 1 ], we discussed the fundamental law of cam design: continuity of acceleration. Advertisement In this post, we are going to derive the exact equations for the Fifth-Degree Polynomial Cam Function . This is the mathematical foundation 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 (x = θ / β) , where x goes from 0 to 1. 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 (θ / β) β = Total angle in sector (rad) To find Velocity (v) and Acceleration (a) , we differentiate with respect to the angle. (Note: The ch...

Polynomial Cam Function (Introduction) - Part 1

In the field of High-Speed Industrial Automation , simple geometric curves often fail. To achieve the smooth, vibration-free motion required by modern CNC machines and textile equipment, engineers must turn to advanced mathematics: Polynomial Cam Functions . Figure 1: High-speed automation requires mathematical precision that simple geometric curves cannot provide. Advertisement The Fundamental Law of Cam Design According to the "Bible" of mechanism design ( Fundamentals of Machine Design, Robert L. Norton ), any high-speed cam must obey two critical rules to avoid catastrophic machine failure: CRITICAL DESIGN RULES: 1. Continuity: The cam function must be continuous through the first (Velocity) and second (Acceleration) derivatives across the entire 360-degree interval. 2. Finite Jerk: The jerk function (the derivative of acceleration) must remain finite across the entire interval. Why "Jerk" Matte...

Timing Diagram (Part 3 - Cycloid Cam Profile Analysis)

In the previous post [ Timing Diagram Part 2: Max Acceleration ] , we calculated the maximum forces acting on a die driven by a cycloid cam profile. We discovered a critical rule of physics: inertial forces are inversely proportional to the square of the time allowed for movement. The Engineering Strategy: If we can extend the indexing angle (time) by allowing Overlap Motion , we can drastically reduce wear. This is the heart of Predictive Maintenance —designing machines that inherently last longer. Advertisement 1. The Cycloid Cam Profile The Cycloidal motion curve is the industry standard for high-speed automation because it has zero acceleration at the start and end of the move. The displacement equation is: h = h m × [ (t / t m ) - 1/(2π) × sin(2π × t / t m ) ] To solve for the Displacement Ratio (percentage of travel), we rearrange it: h / h m = (t / t m ) - 0.159 × sin(6.28 × t / t m ) Figure 1: The ...

Timing Diagram (Part 2 - Maximum acceleration calculation)

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. Advertisement 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...

Timing Diagram (Part 1 - No Overlap Movement)

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 engineering tool that represents the sequential kinematics of mechanism movement. Advertisement It is the standard visualization for engineers to ensure synchronization between cam drives , servo motors , and pneumatic actuators in complex automation cells. The Cost of Poor Timing: By properly designing the timing diagram, we can optimize motion profiles to be smoother even at higher speeds. This directly improves OEE (Overall Equipment Effectiveness) and significantly reduces operational costs. We typically draw the timing diagram using the Master Cam Angle (degrees) on the horizontal axis and the Mechanism Displacement (mm) on the vertical axis. The Goal: Reducing Inertial Forces & M...

High-Speed Automation: The Mechanics of Sankyo SANDEX Indexing

In my design work for high-speed automation, I've frequently relied on indexing boxes from the Japanese manufacturer Sankyo Seisakusho . The SANDEX series is a generic name for their cam units that utilize the superior Roller Gear Cam mechanism . Sankyo's core technology combines a precision-machined globoidal cam with a follower turret fitted with high-capacity needle bearings. To visualize how this robust mechanism works, consider the conceptual model below. Figure 1: A conceptual model illustrating the interaction between the input roller gear cam (bottom) and the output follower turret (top). Advertisement The Superior Mechanics of the Roller Gear Cam As depicted conceptually in Figure 1 , the SANDEX unit uses a continuous rib on the input shaft to drive the output turret. This is a significant upgrade over traditional Geneva mechanisms . Geneva drives suffer from high impact shock at the start and stop of motion due to inhere...

Numerical Differentiation in Excel: Calculating First Derivatives

Numerical methods are powerful tools for mechanical engineering design calculations. In this post, I will demonstrate how to calculate the first derivative (velocity) of a motion profile using numerical methods directly in Microsoft Excel, without the need for specialized math software. While textbooks provide extensive derivations, for practical engineering, we can jump straight to the high-accuracy finite difference formulas. The 5-Point Stencil Formula To calculate the first derivative of a function f(x) with high precision, we use the "Five-Point Stencil" method. This formula utilizes interior points to achieve an error order of h 4 , which is significantly more accurate than standard forward or backward difference methods. f'(x i ) = [ -f(x i+2 ) + 8f(x i+1 ) - 8f(x i-1 ) + f(x i-2 ) ] / 12h Where: i = The current point of interest h = The step size (the distance between points) The smaller the step size ( h ), the higher the a...