Continuous Looping animation - Differing rotational speeds

Question

Just trying to do my first animation and am struggling to make it loop seamlessly. I think the differing rotational speeds of the 2 objects are the thing to overcome but I'm not sure how. I basically want the earth to do one revolution to the teapot's 2 orbits around the earth.

Can anyone have a look at this and advise me?

Thanks in advance.

Answer 1

Driver Based approach.

For the planet I have added a driver to its z rotation.

 pi * frame / 40

where frame is known to the driver namespace as the current frame. The rotation is 0 degrees at frame 0 and 360 degrees (2pi radians) at frame 80.

A satellite object and an orbit circle is added. A follow path constraint, with follow curve and fixed position.

The driver is added to the offset.

(frame / 40) % 1.0

At frame 0 and frame 40 will be at 0 and 1 offset (same position) respectively. The % is python modulus, ie the remainder when divided by one. Related

Ok so now have a planet that revolves once in 80 frames and a satellite that orbits every 40 frames.

To loop the animation, set 1 and 80 as start and end frames.

Answer 2

In order to get a fixed and repeated rotation you can use the f-curve 'Generate' modifier. This allows you to define an equation (that you can precisely tune for the required rotation) for the f-curve rather than basing on keyframes.

To achieve this, once you have added a single keyframe, open the Graph Editor and select the relevant channel (eg, Z-rotation). In the Modifiers panel, select Add Modifier and select 'Generator'.

Set the polinomial to '1' since we want a straight line. The generator defines an equation as y = c + mx where c is a constant and m the multiplication factor for the x value (effectively the 'frame' of the animation).

The rotation is measured in radians - so 2xPi radians is a full rotation.

In order to have your object to make a complete rotation in, say, 50 frames you should enter the 'x' multipler ("coefficient for polynomial") to 2*pi/50 (just type that into the field and press Enter - Blender will calculate it for you and show the result (0.126 in this case)).

Repeat for the other object but choose a suitable number of frames (so there's a common factor). For example, 50 frames for one object and 100 for the other will result in them both getting back to their start rotation after 100 frames.

For your situation with an object orbiting the planet you could setup similar to the following :

In the scene there is a Cube (planet), Suzanne (moon) and Empty (to act as the centre of the moon's orbit). Suzanne is a child of the Empty (select Suzanne, hold Shift, select Empty, press Ctrl+P and choose 'Object' - so rotating the empty will move Suzanne around the orbit.

Now select each object in turn (Cube, Suzanne, Empty) and add a keyframe on the Z-rotation.

Select the Cube, open the Graph Editor (as detailed above), add a Generator modifier and set the X coefficient to 2*pi/100 (rotate once per 100 frames).

Repeat for the Empty but set the coefficient to 2*pi/50 (rotate once per 50 frames).

Repeat for Suzanne to set the rotation of the 'moon'.

Answer 3

Alternative Driver-based Solution

I used this question as an exercise to familiarize myself with drivers. The solution turned out well enough and different enough from the others that I figured I'd post it. I couldn't say whether it has any particular advantage or disadvantage compared to the other driver answer; it's just what I came up with. :)

This is a driver-based solution built on Script Expressions that uses only the primary objects (planet + satellite, no empties or curves).

In preparation use keyframes to animate the "planet" object so it does one rotation around the Z-axis over the course of the animation.

The drivers all target the satellite (Suzanne) and are all based on the planet's rotation. We need at least two: one for the satellite's X location and one for its Y location. If we want the satellite to have a synchronized orbit such that the same side always faces the planet then a third driver targets the satellite's Z rotation.

I created each driver by hovering over the appropriate field in the Object tab in the Properties window, entered Ctrl+D, and selected Manually Create Later (Single). (In 2.8x this will pop a dialog. Just dismiss it by moving mouse away.)

Next, open the Graph Editor (1) (in 2.8x choose Drivers rather than Graph Editor), select one of the drivers from the left panel (2), open the Properties drawer (N) and click the Drivers tab (3).

Create a variable (4) with these attributes (5):

Type: Transform Channel
Name: planetZRot
Object: Planet
Type: Z Rotation
Space: World

Now copy this variable to the other drivers using the "arrow & clipboard" buttons (6).

Configure each driver to have type Scripted Expression (7). The expressions for each of the drivers are as follows.

• X Location: 0 + (cos(planetZRot * m)) * r
• Y Location: 0 + (sin(planetZRot * m)) * r
• Z Rotation: planetZRot * m

Here m is S_rot / P_rot, the ratio of the satellite's rotation to the planet's rotation and r is the radius of the orbit.

Result with m=2 and r=3...