The first step in creating an IK system is to create and link several objects together. You can create links using the Link button on the main toolbar.

With the linked system created, position the child object's pivot point at the center of the joint between it and its parent. For example, the joint between an upper and lower arm would be at the elbow, so this is where the pivot point for the lower arm should be located.

After you create the linked system and correctly position your pivot points, open the Hierarchy panel and click the IK button. Several rollouts open that let you control the IK system, including the Object Parameters rollout shown in Figure 41.1.

Figure 41.1. The IK rollouts let you control the binding of an IK system.

Because child objects in an IK system can cause their parents to move, moving a child could cause unwanted movements all the way up the system to the root object. For example, pulling on the little finger of a human model could actually move the head. To prevent this, you can select an object in the system to be a terminator.

A terminator is the last object in the IK system that is affected by the child's movement. Making the upper arm a terminator would prevent the finger's movement from affecting any objects above the arm.

To set a terminator, select an object and then enable the Terminator option in the Object Parameters rollout.

For Interactive IK mode, you can also enable the Auto Termination option included in the Auto Termination rollout. The Number (#) of Links Up value sets the terminator a specified number of links above the current selection.

The next step is to define the joint constraints, which you specify in the Sliding Joints and Rotational Joints rollouts. By default, each joint has six degrees of freedom, meaning that the two objects that make up the joint can each move or rotate along the X-, Y-, or Z-axes. The axis settings for all other sliding and rotational joints are identical. Defining joint constraints enables you to constrain these motions in order to prevent unnatural motions, such as an elbow bending backward. To constrain an axis, select the object that includes the pivot point for the joint, locate in the appropriate rollout the section for the axis that you want to restrict, and deselect the Active option. If an axis's Active option is deselected, the axis is constrained. You can also limit the motion of joints by selecting the Limited option.

When the Limited option is selected, the object can move only within the bounds set by the From and To values. The Ease option causes the motion of the object to slow as it approaches either limit. The Spring Back option lets you set a rest position for the object; the object returns to this position when pulled away. The Spring Tension sets the amount of force that the object uses to resist being moved from its rest position. The Damping value sets the friction in the joint, which is the value with which the object resists any motion.

Defining joint constraints can be lots of work—work that you wouldn't want to have to duplicate if you didn't have to. The Copy and Paste buttons in the Object Parameters rollout enable you to copy Sliding Joints or Rotational Joints constraints from one IK joint to another.

To use these buttons, select an IK system and click the Copy button; then select each of the joints to be constrained in a similar manner, and click the Paste button. You also have an option to mirror the joints about an axis. It is useful for duplicating an IK system for opposite arms or legs of a human or animal model.

When using applied IK, you need to bind an object in the IK system to a follow object. The IK joint that is bound to the follow object then follows the follow object around the scene. The bind controls are located in the Hierarchy panel under the Object Parameters rollout. To bind an object to a follow object, click the Bind button in the Object Parameters rollout and select the follow object.

In addition to binding to a follow object, IK joints can also be bound to the world for each axis by position and orientation. This causes the object to be locked in its current position so it won't move or rotate along the axis that is selected. You can also assign a Weight value. When the IK computations determine that two objects need to move in opposite directions, the solution favors the object with the largest Weight value.

The Unbind button eliminates the binding.

When Max computes an IK solution, the order in which the joints are solved determines the end result. The Precedence value (located in the Object Parameters rollout) lets you set the order in which joints are solved. To set the precedence for an object, select the object and enter a value in the Precedence value setting. Max computes the object with a higher precedence value first.

The default joint precedence for all objects is 0. This assumes that the objects farthest down the linkage move the most. The Object Parameters rollout also includes two default precedence settings. The Child to Parent button sets the precedence value for the root object to 0 and increments the precedence of each level under the root by 10. The Parent to Child button sets the opposite precedence, with the root object having a value of 0 and the precedence value of each successive object decreasing by 10.

As an example of a kinematics system, you'll start with a backhoe, which is a simple linkage system with tracks that can move forward, a chair housing that can rotate independently, and an arm and bucket that can rotate about a pivot. When you're finished with this tutorial, you can take the backhoe out and dig a hole for a swimming pool. I think you deserve it.

To create an inverse kinematics system for a backhoe, follow these steps:

Figure 41.3 shows the bucket moving. With the Interactive IK mode disabled, any object can be moved and/or rotated, and only the links are enforced.

Figure 41.3. The objects in this scene are part of an inverse kinematics system.

Interactive IK is the method that lets you position a linked hierarchy of objects at different frames. Max then interpolates all the keyframes between the various keys. This method isn't as precise, but it uses a minimum number of keys and is useful for an animation sequence involving many frames. Interactive IK interpolates positions between the two different keys, whereas Applied IK computes positions for every key. Because the motions are simple interpolations between two keys, the result may not be accurate, but the motion is smooth.

After your IK system is established, animating using the Interactive IK method is simple. First, you need to enable the Auto Key button and select the Interactive IK button in the IK rollout of the Hierarchy panel. Enabling this button places you in Interactive IK mode, causing the system to move together as a hierarchy. Then reposition the system in a different frame; Max automatically interpolates between the two positions and creates the animation keys. To exit Interactive IK mode, simply click the Interactive IK button again.

The IK rollout includes several options. The Apply Only to Keys option forces Max to solve IK positions for only those frames that currently have keys. The Update Viewports option shows the animation solutions in the viewports as it progresses, and the Clear Keys option removes any existing keys as the solution is calculated. The Start and End values mark the frames to include in the solution.

IK Preference settings

The required accuracy of the IK solution can be set using the Inverse Kinematics panel in the Preference Settings dialog box, shown in Figure 41.4. You can open this dialog box by choosing Customize

You can also set an Iterations limit for both methods. The Iterations value is the maximum number of times the calculations are performed. This value limits the time that Max spends looking for a valid solution. The Iterations settings control the speed and accuracy of each IK solution.

Note

If the Iterations value is reached without a valid solution, Max uses the last calculated iteration.

The Use Secondary Threshold option provides a backup method for determining whether Max should continue to look for a valid solution. This method should be used if you want Max to bail out of a particularly difficult situation rather than to continue to try to find a solution. If you are working with very small thresholds, you want to enable this option.

The Always Transform Children of the World option enables you to move the root object when it is selected by itself but constrains its movement when any of its children are moved.

Figure 41.4. The Inverse Kinematics panel of the Preference Settings dialog box lets you set the global Threshold values.

Tutorial: Animating a simple IK propeller system

Machines are good examples of a kinematics system. In this example, you animate a simple gear-and-propeller system using the Applied IK method.

To animate an inverse kinematics system with a propeller, follow these steps:

1. Open the Gear and prop.max file from the Chap 41 directory on the DVD.

   This file includes a simple handle and prop system.

2. The first task is to link the model. Click the Select and Link button on the main toolbar. Then drag from each child object to its parent. Connect the propeller to the shaft, the shaft to the gear, and the gear to the handle.

3. Open the Hierarchy panel, and click the IK button. Next constrain the motions of the parts by selecting the handle object. All Sliding Joints can be deactivated, and only the Z Axis Rotational Joint needs to be activated. To do this, make sure that a check mark is next to the Active option. When this is set for the handle object, click the Copy button for both joint types, select the gear object, and click Paste to copy these constraints. Then select the shaft object, click both Paste buttons again, and repeat this process for the propeller.

4. Finally, enable the Auto Key button (or press the N key), drag the Time Slider to frame 100 (or press the End key), and click the Interactive IK button in the Inverse Kinematics rollout of the Hierarchy panel. Then select the Select and Rotate button (E), and drag in the Left viewport to rotate the handle about its Z-axis.

Figure 41.5 shows the propeller system.

Figure 41.5. The propeller rotates by turning the handle and using IK.

Applied IK applies a solution over a range of frames, computing the keys for every frame. This task is accomplished by binding the IK system to an object that it follows. This method is more precise than the interactive IK method, but it creates lots of keys. Because keys are set for every object and every transform, this solution sets lots of keys, which increases the size and complexity of the scene. Each frame has its own set of keys, which could result in jerky, non-smooth results.

To animate using the Applied IK method, you need to bind one or more parts of the system to a follow object, which can be a dummy object or an object in the scene. You do so by clicking the Bind button in the Object Parameters rollout of the Hierarchy panel and selecting an object in one of the viewports. After the system has a bound follow object, select an object in the system. Open the Hierarchy panel; in the Inverse Kinematics rollout, click the Apply IK button. Max then computes the keys for every frame between the Start and End frames specified in the rollout. Click the Apply IK button to start the computation process that sets all the animation keys for the range of frames indicated.

The History Independent (HI) IK solver looks at each keyframe independently when making its solution. You can animate linked chains with this IK solver applied by positioning the goal object; the solver then keyframes the position of the pivot point of the last object in the chain to match the goal object.

You can apply IK solvers to any hierarchy of objects. IK solvers are applied automatically to a bones system when you create the system. You can also choose Animation

When you choose Animation

The first rollout is the IK Solver rollout, shown in Figure 41.6. Using this rollout, you can select to switch between the HI IK solver and the IK Limb solver. The Enabled button lets you disable the solver. By disabling the solver, you can use forward kinematics to move the objects. To return to the IK solution, simply click the Enabled button again. The IK for FK Pose option enables IK control even if the IK solver is disabled. This lets you manipulate the hierarchy of objects using forward kinematics while still working with the IK solution. If both the IK for FK Pose and the Enabled buttons are disabled, then the goal can move without affecting the hierarchy of objects.

Figure 41.6. The IK Solver rollout lets you enable or disable the IK solver.

If the goal ever gets moved away from the end link, clicking the IK/FK Snap button automatically moves the goal to match the end links position. Auto Snap automatically keeps the goal and the end link together. The Set as Preferred Angle button remembers the angles for the IK system. These angles can be recalled at any time using the Assume Preferred Angle button.

When you choose Animation

Displaying IK controls

The IK Display Options rollouts can enable, disable, and set the size of the gizmos used when working with IK solvers. Using this rollout, you can Enable the End Effector, the Goal, the Swivel Angle Manipulator, and the IK solver (which is the line connecting the start and end joints).

Figure 41.7. The swivel angle defines the plane along which the joint moves.

The History Dependent (HD) IK solver takes into account the previous keyframes as it makes a solution. This solver makes having very smooth motion possible, but the cost of time to compute the solution is increased significantly. You can also assign this IK solver to bones systems by specifying the History Dependent solver in the IK Chain Assignment rollout or by choosing Animation

This IK solver shows up as a controller in the Motion panel when the IK chain is selected. The settings are contained in a rollout named IK Controller Parameters, which is visible in the Motion panel if you select one of the end effector gizmos. The end effector gizmo is the object that you move to control the IK chain. It is displayed as a set of crossing axes.

Figure 41.8. Moving the goal for each IK chain makes animating a character easy.

You can access the IK Controller Parameters rollout, shown in Figure 41.9, in the Motion panel. Any parameter changes affect all bones in the current structure. In the Thresholds section, the Position and Rotation values set how close the end effector must be to its destination before the solution is complete. In the Solution section, the Iterations value determines the maximum number of times the solution is attempted. These Thresholds and Iterations values are the same as those in the Preference Settings dialog box, except that they affect only the current linkage. The Start Time and End Time values set the frame range for the IK solution.

Figure 41.9. The IK Controller Parameters rollout sets the boundaries of the IK solution.

The Show Initial State option displays the initial state of the linkage and enables you to move it by dragging the end effector object. The Lock Initial State option prevents any linkage other than the end effector from moving.

The Update section enables you to set how the IK solution is updated with Precise, Fast, and Manual options. The Precise option solves for every frame, Fast solves for only the current frame, and Manual solves only when the Update button is clicked. The Display Joints options determine whether joints are Always displayed or only When Selected.

When you first create a bones system, an end effector is set to the last joint automatically. In the End Effectors section, at the bottom of the IK Controller Parameters rollout, you can set any joint to be a Positional or Rotational end effector. To make a bone an end effector, select the bone and click the Create button. If the bone already is an end effector, then the Delete button is active. You can also link the bone to another parent object outside of the linkage with the Link button. The linked object then inherits the transformations of this new parent.

Click the Delete Joint button in the Remove IK section to delete a joint. If a bone is set to be an end effector, the Position or Rotation button displays the Key Info parameters for the selected bone.

A telescoping spyglass is a good example of a kinematics system that you can use to show off the HD solver. The modeling of this example is also easy because it consists of a bunch of cylinders that gradually get smaller.

To animate a spyglass with the HD IK solver, follow these steps:

Figure 41.10 shows the end tube segment collapsing within the spyglass.

The IK Limb solver was specifically created to work with limbs. It is used on chains of three bones such as a hip, upper leg, and lower leg. Only two of the bones in the chain actually move. The goal for these three joints is located at the pivot point for the third bone. This solver is ideal for game character rigging.

The way this solver works is that it considers the first joint as being a spherical joint that can rotate along three different axes, like a hip or shoulder joint. The second joint can bend only in one direction, such as an elbow or knee joint.

The rollouts and controls for the IK Limb solver are exactly the same as those used for the HI solver covered earlier in this chapter.

Figure 41.10. The HD IK solver is used to control the spyglass.

As an example of the IK Limb solver, you should probably animate a limb, so I've created a simple spider skeleton with not two limbs, but eight. I created this skeleton fairly quickly using four bones for the abdomen; then I created one limb and cloned it three times. Then I used the Bone Tools to connect the leg bones to the abdomen bones, and finally I selected and mirrored the bones on all four legs to get the opposite legs. The hardest part was naming all the bones.

To animate a spider skeleton's leg using the IK Limb solver, follow these steps:

Figure 41.11 shows the spider's leg being moved via the IK Limb solver. The IK Limb Solver provides a simple and quick way to add an effector to the end of a limb, giving you a good control for animating the spider's walk cycles.

The Limb IK solver works well for arms and legs that have a joint in their middle, but it doesn't work well for tails. Tails are unique because they require multiple bones to deform correctly. The Spline IK solver works well for tails, but it also works well for rigging tentacles, chains, and rope.

To use the Spline IK solver, you need to create a chain of bones and a spline path. By selecting the first and last bone and then selecting the spline, the bone chain moves to the spline. Each control point on the spline has a dummy object associated with it. By moving these dummy objects, you can control the position of the bones. At either end of the spline are manipulators that you can use to twist and rotate the bones.

Figure 41.11. You can use the IK Limb solver to control limbs such as legs and arms.

The easiest way to use this IK solver is to select SplineIKSolver from the drop-down list in the IK Chain Assignment rollout while you're creating the bone structure. After the bone structure is complete, the Spline IK Solver dialog box appears. With this dialog box, you can select a name for the IK chain, specify the curve type, and set the number of spline knots. The curve type options include Bézier, NURBS Point, and NURBS CV. You can also select to Create Helpers and to display several different options.

Another way to use this IK solver is with an existing bone structure. To do this, you need a spline curve in the scene that matches how you want the bone chain to look. Then select the first bone where you want the solver to be applied, and choose Animation

The bone structure then assumes the shape of the spline curve. A helper object is positioned at the location of each curve vertex. These helper objects let you refine the shape of the curve.

The IK Spline solver is perfect for creating long, winding objects like snakes or an alligator's tail. For this example, you'll take an existing bone structure and, using the Spline IK solver, make it match a spline.

To create a bone structure for an alligator that follows a spline using the IK Spline solver, follow these steps:

Figure 41.12 shows the bone structure for the gator's tail. You can now control the gator's tail by moving the dummy objects along the spline.

Figure 41.12. The IK Spline solver is perfect for creating objects such as snakes and animal tails.