This is an animation of the leg mechanism designed using function generators to drive the hip and knee joints. A second parallelogram linkage is used to construct a translating leg that allows placement of the foot trajectory where ever the designer chooses.
This is a series of four videos that show how to:
- Specify three positions for the foot of a leg consisting of a hip and knee joint;
- Use three position synthesis to design a four-bar function generator to guide the hip joint;
- Then use three position synthesis to design a second four-bar function generator to guide the knee joint;
- And finally assemble the linkage to determine the trajectory of the foot. Adjusting the lengths of the leg segments, the position of the hip, the specified positions of the input cranks, and the position of the coupler attachments to the input cranks vary the resulting foot trajectory. An example leg mechanism is shown at the end of this video.
Part 1:4 Setting up the design
Part 2:4 Synthesis of the hip function generator.
Part 3:4 Synthesis of the knee function generator.
Part 4:4 Assembly of the leg mechanism, exploration of design variations, and an example final leg design.
The graphical construction of a four-bar function generator that coordinates three input and three output angles is presented in the video below. It is possible to coordinate as many as five input-output angles, but this requires numerical calculations using software like our MechGen FG iOS application.
Our MechGen FG iOS application provides five position synthesis for four-bar linkages. A Demo of the iPad version is provided below. It is also available on the iPhone.
The graphical construction of a four-bar linkage that coordinates two positions of an input crank with two positions of an output crank is presented in this video using Geogebra.
A linkage that coordinates the values of input and output angles is called a function generator. It is possible to design a four-bar linkage to coordinate as many as five input and output angles. However, this requires numerical calculations using software such as our MechGen FG iOS application.
This video adds a skew pantograph to a four-bar linkage in order to reorient and change the size of the coupler curve. The result is a six-bar leg mechanism with a foot trajectory that is a scaled version of the original coupler curve.
In this video, we start with a four-bar linkage and coupler curve and construct an additional crank with a floating link connected to the coupler point. This floating link becomes the leg of the Klann-style leg mechanism. Adjustment of the dimensions of the added links shapes the foot trajectory.
This video starts with a four-bar linkage with a coupler curve that is to be used as the foot trajectory for a leg mechanism. It presents a Geogebra construction of two additional bars, one of which is connected to the coupler point and moves without rotating. This means the bar can be expanded into a leg that places the desired coupler curve where the designer specifies. This is described in Chapter 4 of Kinematic Synthesis of Mechanism.
This video shows the construction of the cubic of stationary curvature. The intersection of the cubic of stationary curvature with the inflection circle, iw Ball’s point which is a coupler point that traces a locally straight line trajectory.
This video also shows how to vary the coupler point and the dimensions of the reference polygon for the four-bar linkage to vary the shape of the coupler curve.
This tutorial constructs the inflection circle for a particular configuration of a four-bar linkage. This construction was recommended by my colleague Gordon Pennock because it is simpler than the one I provide in my book Kinematic Synthesis of Mechanisms.