Mechanical Design Handbook

Many modern engineering applications require components to move in a precise linear fashion, known as " straight-line motion ". Today, we take this for granted. We can simply purchase an off-the-shelf Linear Motion Guide (like the THK model shown to the right) that guides a device accurately along a rail. The manufacturing know-how of linear guide manufacturers has allowed us to expand the range of linear guidance into everything from CNC machines to 3D printers. These Linear Ball Slides are lightweight, compact, and operate with very low sliding resistance and low inertia. The Historical Challenge: Making a Straight Line However, in the late 17th and early 18th centuries—before the development of the milling machine or the planer—it was extremely difficult to machine long, perfectly straight, flat surfaces. For this reason, creating good prismatic pairs (sliding joints) without significant backlash was nearly impossible. During that era, eng...

In [ 3-Position Synthesis with Inversion Method using Unigraphics NX4 Sketch - Part 2 ], we successfully determined the locations of the moving pivots (G and H) relative to our fixed ground pivots (O 2 and O 4 ). However, finding the points is only half the battle. Before we commit to manufacturing or detailed 3D modeling, we must verify that the mechanism actually moves smoothly between all three positions without locking up (toggle positions) or deviating from the path. Constructing the Kinematic Chain Now that we have our four critical points (O 2 , O 4 , G, H), we need to "build" the mechanism links within the NX Sketcher environment: Input Link (Link 2): Draw a solid line connecting the fixed ground O 2 to the moving pivot G. Output Link (Link 4): Draw a solid line connecting the fixed ground O 4 to the moving pivot H. Coupler Link (Link 3): This is the most important part. You must draw a rigid triangle connecting G, H, and the original c...

In the previous introduction , we established the problem: We have fixed mounting points (O 2 and O 4 ) on our machine base, and we need to design a linkage to hit 3 specific positions. Standard synthesis moves the pivots to fit the motion. In Kinematic Inversion , we do the opposite: we virtually move the ground to fit the coupler. By "freezing" the coupler in Position 1 and moving the ground relative to it, we can geometrically find the required link lengths. Step 1: Setup the Constraints Start by drawing your known constraints in the NX Sketcher: 1. The Fixed Ground Pivots (O 2 and O 4 ). 2. The 3 Desired Coupler Positions (A 1 B 1 , A 2 B 2 , A 3 B 3 ). (The red lines in the image below represent the moving coupler in its three positions). Step 2: Inverting Ground Pivot O 2 Now we perform the "Inversion." We need to find where the ground pivot O 2 would be relative to Position 1 if the coupler stayed still. ...